Prison worker Joyce “Tillie” Mitchell had sex at least 100 times in a sewing-shop storage closet with one of the convicted killers she helped spring, a former inmate told The Post — hours after her clueless husband insisted she never could have bedded the escaped criminals.

Mitchell spent her jailhouse days giggling, chatting and showering gifts on convicted cop-killer David Sweat in the Clinton Correctional Facility workplace she was supposed to be supervising, said the former prisoner, Erik Jensen.

She would routinely end her shift by disappearing into the 8-foot-by-15-foot stockroom with the 35-year-old Sweat for at least a half-hour at a time, said Jensen.

“He was getting it on with her,” Jensen said. “Or she was doing sexual favors for him.”

Mitchell, 51, gave the other inmates an unlikely excuse for her storage-closet tête-à-têtes with Sweat — she said they were just counting the clothes made by each prisoner.

But no one was fooled.

“Everyone used to joke with him that he was getting his quiet time with his ‘boo,’ his girlfriend,” Jensen said. “It was like the running joke in the tailor shop.”

Jensen revealed the details of the sex romps after Mitchell’s husband, Lyle, told NBC News that Joyce “absolutely” assured him last week that she never cheated on him with Sweat or double-murderer Richard Matt, 48.

Both inmates remained on the run Tuesday, 17 days after they staged a “Shawshank Redemption”-style breakout from the prison in upstate Dannemora.

Jensen — who served time at Clinton for possessing stolen property from tractor-trailer robberies— worked with Sweat in the workroom known as Tailor Shop 3. The second-floor sewing room is one of eight where inmates stitch together pants, jackets and other garments for prisoners and correction officers.

Joyce made Sweat her head tailor, which put him behind a desk instead of a sewing machine. She often appeared giddy with excitement when they interacted, Jensen said.

“The way I can describe it is in high school, when one of the good-looking jocks looks at the ugly girl or asks her to the prom — that look on her face. She was ecstatic,” Jensen said.

During lunchtime, when the inmates headed off to the mess hall for chow, Sweat would stay behind in the tailor shop with Joyce, Jensen said.

“Mitchell would bring him Subway sandwiches, hamburgers,” he said.

“The day after Labor Day, she brought in barbecue chicken, hot dogs and hamburgers . . . She put it inside a Styrofoam tray to make it look like it came from the mess hall.”

The stockroom where the couple trysted is narrow, with rows of floor-to-ceiling shelving on either side and a desk below a window opposite the door, Jensen said. The window even has a view of the manhole that authorities say Sweat and Matt climbed out of during their elaborate escape.

Jensen, 34, said Joyce and Sweat would rendezvous in the stockroom as often as four times a week, and he estimated they hooked up at least 100 times there during the eight months he himself was locked up there.

Sweat was transferred out of the sewing shop as part of an investigation into his relationship with Joyce.

No charges were ever filed against her due to a lack of evidence.

Mitchell even convinced prison officials to move Sweat’s cell next to Matt’s on the Dannemora “honor block,” CNN reported. Eventually, Matt began wooing Joyce, who agreed to help both men bust out, sources have said.