Rutgers let an eight-point lead at the intermission get away, but after falling behind the Scarlet Knights came back to tie it at 46-46 with 8:03 to play. They did not score another point until just 51 seconds remained in the game.
Cashmere Wright's 3-pointer put Cincinnati in front to stay with 6:38 left and his two free throws in the final minute gave the Bearcats a seven-point lead.
Cincinnati had won just four of its previous eight games after capturing its first 12 contests of the year. The Bearcats climbed to 17-4 for the season and are 5-3 in Big East Conference play.
Kilpatrick scored 19 points and Chikeh Mbodj added 10 for Cincinnati, which survived a 36-percent shooting performance and 17 turnovers.
Myles Mack led Rutgers (12-8, 3-6) with 15 points.