Shabazz Napier had a career-high 27 points to lead Connecticut (14-4, 4-3), which lost for the first time at home this season.
Cincinnati took 26 shots from behind the arc, hitting 11 of them.
Cincinnati led by 12 points in the first half and nine at halftime.
But the Bearcats trailed 57-55 before a 3-pointer by Kilpatrick, one of his five in the game, and a late 10-0 turned that into a 65-57 lead.
A 3-point shot by Napier cut it to 66-63 with just over a minute left, and another tied it with 10 seconds to go.
But the Bearcats took the ball up the court and Kilpatrick calmly launched his shot from behind the top of the key.
Cincinnati led 48-37 just under 4 minutes into the second half when UConn went on its 15-2 run.
A block by Andre Drummond and a layup by Jeremy Lamb at the other end made it 48-44. A two-handed fast-break dunk by Drummond tied it and Roscoe Smith's layup gave the Huskies their first lead of the half at 52-50.
Kilpatrick had eight early points and Cincinnati used an early 8-0 run to take a 21-15 lead. Consecutive 3-pointers by Wright and JaQuon Parker stretched the lead to 10 at 29-19.
Napier kept the Huskies in the game with 13 first-half points, but Cincinnati led 42-33 at the half on a tip-in by Jeremiah Davis just before the buzzer.
Cincinnati is 5-1 on the road and 5-1 in conference play. The Bearcats had won nine of their last 10 games, including consecutive conference wins over No. 10 Georgetown and Villanova. The start is the team's best since joining the Big East in 2005.
Cincinnati has won six of its last eight games against ranked opponents.
Gates starting for the third time since his six-game suspension for his part in the Dec. 10 brawl against Xavier also had 12 rebounds, and held UConn center Andre Drummond to just four points. Drummond was coming off three consecutive double-doubles, making him the first UConn freshman to do that since Corny Thompson back in 1978-79.
Connecticut was playing for the second straight game without freshman point-guard Ryan Boatright. He's the subject of a second investigation this season into his eligibility.
Boatright, who has averaged more than 10 points and three assists in 10 games, was suspended for the first six games of the season for an infraction that involved accepting a plane ticket last year while he was playing AAU basketball.
The school, in a statement, said the latest development "arises from additional information provided by the NCAA that pertains to conditions and events that predate the university's relationship with Boatright."
Without Boatright, UConn relied on Napier and Lamb to handle the ball. Lamb played all 40 minutes and finished with 14 points. Napier played 38, hitting 10 of his 19 shots and adding seven assists.
Connecticut and Cincinnati had not played since UConn's 69-58 win in the third round of the NCAA tournament last March, part of the Huskies 11-0 postseason run to the national title.
Connecticut plays it final nonconference game of the season Saturday at Tennessee. Cincinnati travels to West Virginia.