The Post’s discovery of a hot sauce bottle that reeked of bleach at the scene of Jussie Smollett’s alleged hate-crime hoax turned out to be a key piece of evidence, a police report revealed Wednesday.

Chicago cops initially pooh-poohed the finding on Feb. 7 — nine days after the “Empire” star claimed he was attacked by Trump-loving bigots who splashed him with the cleaning fluid.

“Are you trying to do our job?” sneered one detective when reporter Gabrielle Fonrouge alerted police that she’d found the bottle.

She wasn’t, but, as it turns out, she had.

One of the two brothers who said they were paid by Smollett to stage the attack “was shown a large photograph taken of the El Yucateco Hot Sauce bottle,” according to police reports released Wednesday under the Freedom of Information Act to outlets including CWBChicago.

The alleged co-conspirator “stated that indeed was the bottle he filled with bleach and poured on Smollett,” the paperwork revealed.

Neither brother has been criminally charged.

Wednesday’s revelation came despite initial skepticism of the reporter’s detective work.

“It’s highly unlikely that they missed anything that night,” one cop said at the time.

“They already took everything from the scene.”

Fonrouge was asked: “Did you sniff all these bottles? What made you think this one?”

“What else did you find? Should we process all these cigarette butts?” said a detective — who later groused while waiting for a crime-scene technician to arrive, “There goes my dinner plans.”

The Chicago Police Department confirmed on Wednesday that the brothers who staged the attack admitted they used that bottle.

“Those details were given during the interrogation when the brothers confessed to being accomplices in this hoax,” spokesman Anthony Guglielmi told The Post.

The spokesman also said the department takes the detective’s dismissive attitude toward the key piece of evidence “very seriously.”