Dioubate sank 4 of 7 shots, 6 of 10 free throws and added five steals for the Wildcats (7-4). Both subs had nine points after halftime to rally the Wildcats from a 39-32 deficit.
Otega Oweh scored 10 points, the lone Wildcats starter to reach double figures.
Lamar Wilkerson and Tucker DeVries each scored 15 points to lead the Hoosiers (8-3). Tayton Conerway scored 11.
Wilkerson hit two 3-pointers and scored 12 in the first half to help Indiana take a seven-point lead into the break. Nobody had more than five points for Kentucky and reserve Kam Williams was the only one with multiple baskets.
The Wildcats shot 32% in the first half and missed 8 of 9 from beyond the arc. The Hoosiers shot 41% but missed 11 of 14 from distance.
DeVries' layup upped Indiana's advantage to 49-42, but Dioubate grabbed offensive rebounds and scored twice to finish a 10-0 run and Kentucky took the lead with 11:31 left to play and never trailed again.
Neither team shot 40% from the floor. Kentucky made 3 of 15 from beyond the arc, while the Hoosiers were 4 for 24. Indiana was 26 for 29 from the foul line, while the Wildcats made 25 of 38.
Up next
Indiana: Hosts Chicago State on Saturday.
Kentucky: Hosts No. 22 St. John's on Saturday.