The Bearcats trailed by 11 points midway through the second half of the quarterfinal but rallied behind Yancy Gates, who scored 23 points in his back-and-forth big-man duel with Henry Sims.
Gates scored twice in the final 2 minutes of regulation to give the Bearcats their first lead since midway through the first half. The Hoyas' Otto Porter sent the game to overtime when his jumper bounced in with 3.6 seconds remaining.
Sims, who had 22 points and 15 rebounds, hit a layup at the buzzer to send the game to the second OT for the Hoyas (23-8).
The Bearcats (23-9), seeded fourth, face second-ranked Syracuse in Friday's semifinals.
Cincinnati won despite missing 19 of 21 3-point attempts. Dion Dixon, who scored 22 points in the teams' first meeting, was 4 of 17 from the field, 0 of 6 from behind the arc and 5 of 9 from the foul line.
After a timeout with 1:56 left in regulation, Cincinnati got the ball inside to Gates, who scored over Sims to pull Cincinnati within a point. Then when Wright missed a drive with 38 seconds remaining, Gates put it back for a 53-52 lead.
Dixon made the front end of a one-and-one with 25.9 seconds to go but missed the second. The fifth-seeded Hoyas chose not to call a timeout, and with the clock winding down, Sims found Porter open for a short jumper.
The Bearcats tried a long pass to Gates but he couldn't corral the ball at the foul line. The 6-foot-9, 260-pound senior chased it down and was able to launch an off-balance 3-point attempt just before the buzzer, but completely missed the rim.
Dixon again made just one of two free throws with 19.7 seconds left in the first OT to put Cincinnati up 62-60.
After a timeout, the Hoyas couldn't get their offense going as the clock dwindled. The 6-foot-10, 245-pound Sims found himself with the ball at the top of the key, so the big guy put it on the floor. With long stride after long stride, he barreled toward the basket as the seconds ticked away, releasing a layup just before the buzzer to send the game to a second OT.
Markel Starks' jumper for Georgetown tied it at 68-68 with 62 seconds left in the final period.
The teams tied with South Florida for fourth place during the regular season, with the Bearcats winning the tiebreaker to earn a double bye in the Big East tournament for the first time since joining the conference for the 2005-06 season. The Hoyas beat 13th-seeded Pittsburgh 64-52 on Wednesday.
The Bearcats' won the teams' only meeting during the regular season, beating the Hoyas 68-64 on the road Jan. 9.