Cincinnati (9-3) had lost all five previous games against UConn (9-3). The Bearcats led by 11 points before the Huskies made a late run, tying it on Kemba Walker's 3-pointer with 9.4 seconds to go.
Stephenson dribbled into the lane and was fouled by Gavin Edwards as the buzzer sounded. After a review, the officials put seventh-tenths of a second on the clock, Stephenson went to the line and made both, finishing with 21 points.
Jerome Dyson scored 24 points and Stanley Robinson added 22 as UConn lost its scoring balance during its first true road game of the season.
It was a measuring-up game for Cincinnati, which expects to hold its own in the Big East and get back to the NCAA tournament for the first time since 2005, when Bob Huggins was still the head coach. Stephenson, who went 7-of-7 from the line, made the two shots that put them over the top.
The Bearcats knew it would come down to their front line. In Cincinnati's wins over then-ranked Vanderbilt and Maryland, the front line dominated the boards. In other games, it got shoved around. This time, it held its own.
Deonta Vaughn, who went through a 3-of-23 shooting slump from behind the arc, made consecutive 3s that started a 12-2 run and put the Bearcats ahead 30-18. Vaughn yelled and pumped his fist after the second 3, showing his confidence was back.
Robinson had a basket and a three-point play during a 9-0 run that got it down to 30-27 and turned it into a back-and-forth game. Neither team got into an offensive flow in the half, which ended with Cincinnati ahead 36-35.
Vaughn had 10 points, matching his high for any opening half this season, and finished with a season-high 17.
Vaughn hit another 3 during a nine-point run that rebuilt the lead to 47-37 early in the second half. The Huskies managed only one basket during the opening 5:26 of the half, going 1-of-9 with three turnovers during that span.
The Bearcats led 61-50 with 8:10 left when UConn made its last surge behind Dyson, who scored 10 points during a spurt that cut it to 67-63 with 2:27 to go.