Jimmy Butler scored five of his game-high 20 points in overtime, including two on a breakaway dunk off an inbounds pass from Lazar Hayward. Darius Johnson-Odom also scored 20 for Marquette (17-9, 8-6 Big East).
After Butler's dunk put MU up 77-73, Rashad Bishop hit a three with 7.9 second remaining to draw the Bearcats (15-11, 6-8 Big East) within one. Cincinnati fouled immediately, and MU's Maurice Acker sank both shots for what would be the final points of the game.
Deonta Vaughn got a good look at a three in the final second to send the game to a second overtime but missed.
The game went into overtime after Hayward hit a three-pointer with 28 second remaining in regulation to tie the score at 67.
"It was a very well contested shot," Marquette head coach Buzz Williams said. "It was a big shot by a big-time player, at a big-time moment in time."
Hayward shot only 4-of-13 from the field, but made his final three baskets, including a second three-pointer in the extra frame.
"He means everything to our team," Williams said. "Everyone has tremendous faith in him."
Marquette was also aided by a 16-of-17 effort from the free throw line. Cincinnati went only 8-of-16 from the foul line.
"That pretty much sums it up," Cincinnati head coach Mick Cronin said. "We have got to make some free throws. It's really hurt us in games this year."
Hayward tallied 13 points and 10 boards for Marquette, and Joe Fulce tied a career high with 13 points.
"I thought Joe was as good as he's been as a Divison-I player," Williams said.
The back-and-forth contest, which featured 10 ties ad 12 lead changes, started with a series of huge momentum swings in the first half.
After the Golden Eagles used a 17-0 run to go up 31-18 midway through the half, the Bearcats responded by closing the half on a 21-2 run to lead 39-33 at the break. Cincinnati shot 54 percent from the field in the first half, while Marquette missed its last eight shots leading up to the break.
In the second half, Cincinnati led by as many as 8 points – on a jumper by Yancy Gates with 17:24 remaining – but Marquette quickly closed the distance and kept the score close before retaking the lead, 59-58, on a three-pointer from Acker with 7:37 to play.
The teams traded leads three more times before Hayward's shot to end regulation.
Cincinnati scored 20 points off 11 Marquette turnovers. The Bearcats' bench also outscored Marquette's 45-13, though perennial Bearcat starters Vaughn and Gates wound up coming off the bench for UC.