Alex Kirk finished with 15 points and seven rebounds and blocked Sean Kilpatrick's potential game-winner just before the buzzer, as New Mexico went into Fifth Third Arena and handed No. 8 Cincinnati its first loss in a 55-54 defensive slugfest.
Kendall Williams scored 14 of his 16 points in the second half, while Tony Snell added 10 points, including a late go-ahead jumper for the Lobos (13-1), who fell out of the top-25 after getting upset by South Dakota State last week.
Kilpatrick paced Cincinnati (12-1) with 15 points, while JaQuon Parker and Cashmere Wright chipped in 14 and 12 points, respectively.
The Bearcats, who entered Thursday as one of five undefeated teams remaining, shot just 31 percent from the floor in having their 13-game home winning streak snapped.
"To come in here and hold them to 54 points on 31 percent shooting that's pretty pleasing for a basketball coach. You really appreciate the effort your guys gave," New Mexico head coach Steve Alford said.
It was a two-possession game the entire second half, with the lead changing hands six times in the last six minutes.
The last exchange came when Snell made a deep jumper from the baseline for a 55-54 edge with 2 1/2 minutes to go.
Kilpatrick and Wright each missed from long range on the next two Cincinnati possessions, and Williams drew iron on a contested mid-range jumper with time winding down. Parker was fouled with 15.7 seconds remaining after grabbing the rebound on Williams' miss, and the Lobos still had three more fouls to give before reaching the penalty.
After two more fouls were committed, the Bearcats called timeout with 4.5 ticks showing. Kilpatrick inbounded the ball under the basket to Cheikh Mbodj, who gave the ball back to Kilpatrick in the corner before setting a pick.
Kirk came off Mbodj and got a hand on Kilpatrick's 3-point attempt, and by the time Mbodj grabbed the loose ball, time had expired.
"I thought I had (Kirk), I could have drove him left but I didn't," Kilpatrick said of the final play.
Both teams struggled offensively in the first half, with Cincinnati shooting 5-of-26 (19 percent) inside the arc, and New Mexico's struggles summarized by Chad Adams airballing a potential go-ahead 3-pointer in the final minute.
The Bearcats never trailed in the opening 20 minutes, thanks in part to their five 3-pointers, and went into the break carrying a 26-22 lead.
Williams, the Lobos' leading scorer, was held without a field goal in the first half (0-for-4), but hit a pair from behind the arc in the early stages of the second, and New Mexico took its first lead, 34-32, on Kirk's layup 5 1/2 minutes in.
This was New Mexico's second win over a Big East opponent this season, having defeated Connecticut in the championship game of the Paradise Jam ... Cincinnati shot 11-of-26 (42 percent) from behind the arc and 9-of-38 (24 percent) inside it ... The Bearcats only shot four free throws and made three ... New Mexico was 6-of-11 from the foul line ... Cincinnati opens Big East play at Pittsburgh on New Year's Eve ... New Mexico has a road tilt at Saint Louis on New Year's Eve before hosting UNLV in its Mountain West Conference opener on Jan. 9.