The Bearcats (10-3) trailed by 12 with 6 minutes to go, but went to a full-court press and got a three-point play and the winning layup by Wright in the closing minute at a downtown arena where Cincinnati has won its last 17 games.
Oklahoma (9-2) had a chance to win it, but top shooter Steven Pledger missed a long 3 with a few seconds left. Pledger, who averaged 19.8 points and led Division I guards with a 57.5 shooting percentage coming in, was just 4 of 12 for 11 points against the Bearcats.
Andrew Fitzgerald led the Sooners with a season-high 18 points. Romero Osby added 12.
Dion Dixon had 18, and Sean Kilpatrick added 17 for Cincinnati. Wright made only 3 of his 14 shots, including the two biggest ones.
His three-point play gave Cincinnati only its second lead of the game, 54-53, with 39 seconds left. Osby made a layup that put Oklahoma back ahead with 20 seconds to go. Wright then drove past Osby for the winning layup.
Cincinnati hasn't lost at US Bank Arena since 1997. A crowd of 4,439 - the smallest for a Bearcats home game this season - reveled in the late comeback.
Cincinnati was playing its first challenging game since a 23-point loss at Xavier on Dec. 10, which ended with a brawl and eight players suspended in all. With starting forward Yancy Gates and center Cheikh Mbodj serving six-game suspensions, the Bearcats have reinvented themselves, going to a four-guard offense that worked well against overmatched opponents.
The Bearcats won handily against Wright State (6-8), Radford (1-11), Arkansas-Pine Bluff (1-9) and Chicago State (0-13), scoring 297 points in the last three games. Gates and Mbodj will serve out their suspensions in their Big East opener at Pittsburgh on Sunday.
Against the Sooners, the fire-away approach fizzled until the final minutes. Cincinnati shot only 27.9 percent from the field and went 7 of 30 from behind the arc.
The Bearcats led for only 17 seconds in the first half, which ended with Oklahoma ahead 24-19. Cincinnati had as many field goals as turnovers - seven each - in the half.
Fitzgerald had six points during a 16-5 run that gave the Sooners a double-digit lead that vanished down the stretch. Oklahoma twice missed the front end in the bonus, fueling a 14-2 spurt by Cincinnati that made it come down to the final minute.
Oklahoma had 18 turnovers in all that set up 16 points for Cincinnati.