It took a Manhattan jury just half a day today to convict an ex-NYPD cop of seducing and raping a runaway 14-year-old girl he’d taken up to his Inwood apartment after finding her sobbing and shivering on a bench outside.

Darrin Nemelc, 44, rocked his head back and stared at the courtroom ceiling in anguish as the jury forewoman read the verdict. His teenaged daughter and his wife of 13 years both burst into tears in the audience.

Ordered held without bail by Manhattan Supreme Court Justice Ronald Zweibel, Nemelc now faces up to seven years prison when he is sentenced for statutory rape and related criminal sex act charges on Feb. 27.

“I never asked for it, but at the same time, I was kind of curious,” the girl had testified in her childlike voice last month of acquiescing to Nemelc’s advances in his empty apartment.

Nemelc had first denied any contact with the girl. But when saliva swabbed from the girl’s breast matched his DNA profile, he told cops that all he’d done is let “the little white girl” use his bathroom just after midnight on New Year’s Day, 2011.

Complicating matters was that the girl had serious psychological problems stemming from the tragic death of her mother, and that the swabbed saliva also contained fragments of the DNA from two unidentified persons.

Defense lawyer Jeffrey Chabrowe told jurors in closing arguments that all three foreign DNA profiles must have been transferred onto the girl when she used a bathroom towel. Prosecutors told jurors that stray cells may have transferred onto the girl’s breast when she wrapped herself in a blanket after the assault.

Jurors were shown photos of the girl’s genital abrasions, and heard her describe Nemelc’s chest tattoo and nipple piercing, just as she had to cops on the day of the attack.

Nemelc’s lawyers suggested to jurors that upon bringing the girl up to his apartment — just to use the bathroom — he had stripped simply because the apartment was warm, and that’s how the girl saw the tattoo and piercing.

“There is no reason any adult man would have his shirt off,” prosecutor Rena Paul told jurors in closings. “There is not a hot enough apartment in New York City to justify it,” she said.

“He thought she would never tell anyone,” the prosecutor added. “She would be ashamed and confused and she would never tell anyone. And if she did, who would believe her?”

Nemelc was a cop for seven years before leaving the NYPD in 1999 and taking a job with the MTA.

“The defendant preyed upon a 14-year-old girl who was by herself in the middle of the night, cold, and clearly troubled,” said District Attorney Vance. “Instead of calling the police or her family, the defendant took her back to an empty apartment, where he isolated her, manipulated her, and then raped her. The victim was extraordinarily courageous to come forward and tell the jury her traumatic story. I thank the jurors for their service and attention throughout this very difficult trial.”