Jamie Foxx on that time Michelle Monaghan broke one of his teeth

About an hour into the new thriller “Sleepless,” Jamie Foxx and Michelle Monaghan beat the crap out of each other. It’s a knock-down, drag-out smackdown in a hotel room, with broken furniture and each one taking turns delivering the other a perfect blow.

“She kicked my ass,” Foxx tells us. “Michelle socked me in the mouth, for real.”

No, seriously: Michelle Monaghan punched Jamie Foxx in the mouth.

“I had just had it with him,” Monaghan adds, laughing. “He was having too good of a time, so I put him in his place. I chipped his tooth.”

Or they just befell what can happen to anyone doing a perfectly choreographed fight, be it a movie or a school play. The good news is Foxx’s best friend is a dentist, and he happened to live in Atlanta, where they were filming. This savior grabbed his spackle and made the tooth right again.

“It didn’t hurt our relationship,” Foxx says of his costar. “But it took a minute.”

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As it happens, the two actors have a history, of sorts. They both appeared in the 2010 comedy “Due Date,” the road trip comedy pairing Robert Downey Jr. with Zach Galifianakis. They even played a couple. Not that they shared any scenes together. The only time they met was when they shot a couples picture shown briefly in the film.

Their characters in “Sleepless” have a very different relationship. Foxx plays Vincent Downs, an undercover cop who’s spent years infiltrating a world of corrupt detectives. He inadvertently steals cocaine from a powerful drug kingpin, who then kidnaps his son (Octavius J. Johnson), demanding he return the goods. So begins a twisty thriller largely set in a high-end casino, in which Vincent squares off against scary heavies (like Scoot McNairy) as well as Monaghan’s Jennifer, a dogged detective who doesn’t realize our hero’s undercover, and wants to take him down.

“We’ve seen this kind of movie before, but we put our imprint on it,” Foxx says. We’re not trying to reinvent the wheel; we just put some new spokes on it.”

Even better: It’s a straight-up thriller, not something that only exists to create a franchise. “It was wonderful to know we were going to do this one time and one time only,” the Oscar-winner jokes.

Foxx has played cops before — the posters for “Sleepless” look vaguely similar to the ones for 2006’s “Miami Vice,” in which he played Tubbs — but for Monaghan it was new. She has action on her résumé (“The Bourne Supremacy,” “Mission: Impossible III”), but those films kept her on the sidelines or put her in peril. Her character here is strong and punchy.

“It’s a role you don’t see that often: a woman who’s a single woman, doesn’t have kids — that’s kind of rare in Hollywood,” Monaghan says, with a knowing laugh. “She’s a woman living in a man’s world, and she’s frustrated and damaged and slightly flawed.”

For her, the action was hard, but not un-welcome. “It’s fun to push yourself,” she says. She was an active kid, which didn’t entirely help on this gig. “I grew up with brothers. I was a little rough and tumble, I suppose — a bit of a tomboy. But this was another level. You’re doing things with slight precision, so you don’t get hurt or hurt other people. It takes a lot of concentration and dedication. But it’s a role. It’s my job.”

Even for someone as experienced with action as Foxx, “Sleepless” could be tough. He has three big mano-e-mano tussles, which isn’t easy for any actor.

“I had to go there. I was in the jungles, you know — like in the rain forest of my mind, catching the spirits so we could get through it,” he says. Even when he’s not punching and kicking people, he had to be on the run from a particularly tireless henchman. “I haven’t had a white man chasing me that long since I was young.”