On the night before her shocking death, Dorothy Kilgallen, a star panelist on the hit TV game show “What’s My Line?,” correctly guessed the occupation of a mystery guest: a woman who sold dynamite.

The glamorous, razor-sharp Kilgallen delighted viewers, but behind the scenes, the dogged and courageous reporter was hot on the trail of the biggest story of her life: the assassination of President John F. Kennedy.

The morning after that show, on Nov. 8, 1965, the 52-year-old newspaper columnist hailed by The Post as “the most powerful female voice in America” was dead in her Manhattan town house. Her body was found sitting up in a bed, naked under a blue bathrobe, with the makeup, false eyelashes and a floral hair accessory she had worn on TV still on.

After an autopsy, the city’s chief medical examiner, James Luke, put on Kilgallen’s death certificate: “Acute Ethanol and Barbiturate Intoxication, Circumstances Undetermined.” Luke ruled her death accidental, caused by a combination of sleeping pills and booze.

Quickly closing the case, the city left a tarnished image of Kilgallen as a possible drug abuser and alcoholic.

The truth is far more complex and ominous, contends lawyer and veteran author Mark Shaw, whose exhaustively researched, true-life whodunnit, “The Reporter Who Knew Too Much” (Post Hill Press/Simon & Schuster), comes out Tuesday.

Shaw makes a compelling argument that Kilgallen was the victim of foul play, likely orchestrated by New Orleans Mafia don Carlos Marcello, who feared the results of her 18-month investigation for a tell-all book that would accuse Marcello of masterminding the JFK and Lee Harvey ­Oswald assassinations.

The possibility that Marcello was responsible for JFK’s death came up in the 1991 Oliver Stone movie “JFK,” but New Orleans District Attorney Jim Garrison, who launched a probe, dismissed the idea. “He missed it,” Shaw says. “He didn’t have access to Kilgallen’s research.”

Kilgallen died weeks before a planned second trip to New Orleans for a meeting with a secret informant, telling a friend it was “cloak and daggerish.”

“I’m going to break the real story and have the biggest scoop of the century,” she told her ­lawyer.

Her death brought all that to a halt. “The killers won, because she was eliminated and erased from any historical record about the JFK assassination,” Shaw says. Her JFK book was never ­published.

Citing his findings after three years of research, Shaw is now calling on the Manhattan District Attorney’s Office to resurrect and fully investigate the Kilgallen case.

“Murder is murder whether it happened five days or 50 years ago,” Shaw says. “Victims have rights, and Dorothy was denied hers because there was no investigation.”

Kilgallen is best known for her role on “What’s My Line?” — the 1950s and ’60s CBS show watched by 25 million every Sunday night — with episodes still popular on YouTube. She also co-hosted a radio variety show, “Dick and Dorothy.”

But when asked by TV interviewer Edward R. Murrow about her favorite career, the media icon replied, “My first love is the newspaper, and always will be.”

The daughter of journalist James Kilgallen, Dorothy wrote the Voice of Broadway column for the New York Journal-American, which was syndicated to 200 papers nationwide. She also covered high-profile murder trials, including the case of Dr. Sam Sheppard, who denied killing his pregnant wife — and inspired the smash TV series “The Fugitive.”

Kilgallen wielded power. She single-handedly led Sheppard’s murder conviction to be overturned by the US Supreme Court after she told defense lawyer F. Lee Bailey that when the trial started, Judge Edward Blythin called her into his chambers to get her autograph and blabbed: “It’s an open-and-shut case. He’s guilty as hell.”

An A-list celebrity herself, Kilgallen and her husband, Richard Kollmar, hosted lavish parties with guests ranging from actress Jayne Mansfield to Beatle George Harrison. Her marital problems and longtime affair with pop singer Johnnie Ray were fodder for gossip. She cultivated extensive sources, including underworld figures such as New York Mafia boss Frank Costello. Ernest Hemingway, a friend, called her “the greatest woman writer in the world.”

“She broke the glass ceiling before the term was fashionable,” juggling multiple careers — and earning today’s equivalent of millions of dollars a year — while raising three kids, Shaw says.

JFK’s assassination on Nov. 22, 1963 — two years before her own death — devastated Kilgallen, who had visited the president in the White House with her young­est son, Kerry, and considered Kennedy a friend.

“The American people have just lost a beloved president,” she wrote in her column a week after he was shot while riding in a Dallas motorcade. “It’s a dark chapter in our history, but we have the right to read every word of it.”

Kilgallen, who called “laughable” the Warren Commission’s conclusion that Oswald acted alone, launched her own probe. She compiled a thick file of evidence, interviews and notes, ­always keeping it close or under lock and key.

After her death, the dossier was nowhere to be found.

“Whoever decided to silence Dorothy, I believe, took that file and burned it,” Shaw says.

In a letter to Manhattan District Attorney Cyrus Vance Jr. to be delivered Monday, Shaw cites fresh evidence unearthed by him and others.

It includes never-before-released lab results from Kilgallen’s autopsy he obtained under the Freedom of Information Law.

They reveal the presence of two additional barbiturates in Kilgallen’s system — Tuinal and Nembutal — not just the first-reported Seconal, a sleeping pill for which she had a prescription. The tests also revealed a powder residue on a glass found at her bedside, suggesting that someone opened capsules and poured drugs into her drink, Shaw writes.

Dr. Michael Baden, who later became the city’s chief medical examiner, told a prior author, Lee Israel, that the dosage in Kilgallen’s bloodstream was the stunning equivalent of “15 to 20” 100-milligram Seconal capsules.

“The amount of barbiturates was more than enough to kill her,” Baden confirmed to The Post. But, he said, cops ruled out suicide and found “nothing suspicious about the death. There was no suggestion that this was a ­homicide.”

Shaw raises doubts. Two toxicologists who worked in the Brooklyn Medical Examiner’s Office, Shaw learned, discovered the extra barbiturates in lab tests three years after Kilgallen’s death but did not alert authorities.

The Brooklyn office did Kilgallen’s autopsy — not the office in Manhattan, where she died — an unusual move that was never explained. The Brooklyn office was tightly controlled by the mob, Dr. Steven Goldner, who worked in that office, told Shaw.

“They deliberately sent Kilgallen’s body to Brooklyn as part of the cover-up,” Shaw says.

Someone, Shaw concludes, must have spiked the vodka-tonic that Kilgallen drank the night before she died — either at the Regency Hotel, where the “What’s My Line?” cast and guests gathered after the show, or more likely in the bedroom, where the glass with powdery residue was found.

An FBI file on Kilgallen, which Shaw also obtained under the Freedom of Information Act, reveals she was under surveillance.

Then-FBI Director J. Edgar Hoover bristled at Kilgallen’s columns in 1959, when she traveled to Miami’s Little Havana and interviewed Cuban exiles about their hatred of Cuban dictator ­Fidel Castro. She did so defiantly, because the US supported Castro at the time.

After JFK’s death, she repeatedly challenged the “Oswald alone” theory.

“WRONG,” Hoover scribbled next to one of her clippings.

Kilgallen jumped at the chance to cover the trial of Jack Ruby, the Dallas bar owner who shot ­Oswald in the stomach at Dallas police headquarters. She was the only reporter at the trial to interview Ruby. His lawyer, Melvin Belli, let her speak to Ruby twice. The gifted wordsmith wrote:

“Jack Ruby’s eyes were as shiny brown-and-white bright as the glass eyes of a doll. He tried to smile but his smile was a failure. When we shook hands, his hand trembled in mine ever so slightly, like the heartbeat of a bird.”

Kilgallen infuriated Hoover in 1964 when she obtained and published Ruby’s testimony to the Warren Commission, which held closed-door hearings on JFK’s murder, before its official release. She never divulged who gave her the transcript, vowing, “I’d rather die than reveal the source.”

Shaw obtained more than 50 videotaped interviews — now posted at thedorothykilgallenstory.org and thereporterwhoknewtoomuch.com — conducted by investigative reporter Kathryn Fauble and a colleague who looked into Kilgallen’s death. They include Kilgallen’s close confidants, full-time hairdressers Marc Sinclaire and Charles Simpson; Ruby co-counsel Joe Tonahill; and Katherine Stone, the “What’s My Line?” dynamite saleswoman. Stone was one of the last people to see Kilgallen alive, huddling at the Regency Hotel bar with a “mystery man” after the show.

She never divulged who gave her the transcript, vowing, ‘I’d rather die than reveal the source.’

Simpson said Kilgallen told him before her aborted trip to New Orleans: “If the wrong people knew what I know about the JFK assassination, it would cost me my life.”

Kilgallen told Sinclaire she had gotten “threats.” Fearing for her life and her family, she bought a gun. It was Sinclaire who found Kilgallen’s body at about 9 a.m. in a bedroom in which she never slept, he said.

Shaw contends that the death scene was “staged,” with an empty sleeping-pill bottle and a drinking glass on the nightstand. He theorizes that Kilgallen’s killer had accompanied her into the apartment. Cops never searched for fingerprints, he learned.

Shaw identifies the mystery man at the Regency Hotel as Ron Pataky, a flamboyant Ohio newspaper columnist with a propensity for violent disputes who befriended Kilgallen. Shaw believes Kilgallen had an affair with Pataky, who was 12 years her junior, based on love notes she sent him. But their relationship soured when she suspected Pataky was leaking her JFK assassination ­evidence to her targets.

Forty years after Kilgallen’s death, Pataky penned two poems that, Shaw believes, suggest his involvement as a plant. The first, “Never Trust a Stiff at a Typewriter,” includes the line, “Somebody who’s dead could tell no tales.” The second, called “Vodka Roulette,” typed next to the image of a bartender mixing drinks, reads, “Make one of ’em poison.”

Pataky admits a close friendship with Kilgallen but flatly denies an affair, his presence at the Regency that night, or any involvement in her death. “I loved Dorothy dearly,” he wrote to Shaw last week.

But authorities should interview Pataky and others as part of a deeper look into how and why she died, Shaw argues.

Shaw’s interest in Kilgallen was sparked while researching a book on Belli, Ruby’s attorney. A friend of the lawyer recalled that Belli remarked after Kilgallen’s death: “They’ve killed Dorothy; now they’ll go after Ruby.”

Shaw, who knew Kilgallen only from “What’s My Line?,’’ was flabbergasted to learn about her JFK probe. He eventually dove into her story and became as ­obsessed as she was to pursue justice.

“Now I’m trying to be Dorothy — and be her voice,” Shaw said. “Hopefully, that voice will be heard, an investigation will be done, and the truth will be told.”