The Bearcats (5-2), playing their first road game this season, erased an 11-point deficit early in the second half with a 16-4 run capped by Dixon's layup, giving Cincinnati a 39-38 lead with 10:40 remaining.
Georgia (4-4), which has lost three straight, scored just three field goals after Gerald Robinson's layup put the Bulldogs up 38-31 with 13:02 left.
Kentavious Caldwell-Pope led Georgia with 16 points, but was scoreless in the second half before his 3 cut the lead to 55-51 with 8.8 seconds remaining. Robinson added 12 points for the Bulldogs.
Kilpatrick's two free throws with 7.5 seconds to play ended the scoring.
Cincinnati, which won its second straight game, is off until Dec. 10, when it visits crosstown rival Xavier.
Georgia hosts Georgia Tech on Wednesday.
Cincinnati, which was playing the Bulldogs for the first time, showed its experience in the second half, shutting down Georgia's motion offense with a tight zone. Sporting a bigger front line, the Bearcats repeatedly stepped in Georgia's passing lanes and held the Bulldogs to 28.6 percent shooting (6 of 21) in the final 20 minutes.
Georgia had eight turnovers and three assists in the second half.
The Bearcats went nearly eight minutes without a field goal in the first half before Kilpatrick's 3 from the right wing cut Georgia's lead to 15-12.
Dixon followed with a 3 from the left corner, but Caldwell-Pope soon scored his sixth straight point to make it 26-17.
Yancy Gates, who began the game leading Cincinnati with a 14.2 scoring average and a 9.3 rebounding average, finished with five points and eight rebounds. He had scored in double figures in 14 of his last 15 games.