Ashton Gibbs added 15 points for the Panthers (14-9, 3-7).
Kevin Jones scored 21 points and grabbed 13 rebounds to get his 16th double-double of the season for West Virginia (15-8, 5-5), which lost its third straight conference game.
West Virginia held a 17-9 lead in the first half when Pitt went to work.
The Panthers outscored the Mountaineers 9-2 to trail 19-18 with 6:08 to go.
The teams went through four more lead changes and two ties en route to Pitt's 33-29 halftime advantage.
The Panthers scored the first two baskets of the second half and led 37-31 before Dante Taylor was fouled while making a layup.
Official Sean Corbin called a technical foul against West Virginia coach Bob Huggins, and after Ashton Gibbs made one of the two technical shots and Taylor made his free throw, the Panthers led 41-31 at the 17:40 mark.
West Virginia outscored Pitt 14-7 over the next seven minutes to trail 48-45 on a jumper by Jones with 10:45 to go.
The Mountaineers cut it to 54-52 when Kilicli blocked a Pitt shot, which Hinds turned into a layup with 8:12 remaining.
Jones' jumper at 7:31 again pulled West Virginia within two, 56-54.
Kilicli picked up a loose ball under the basket and pulled West Virginia within 70-66 with 17 seconds left.
But Keaton Miles picked up his fifth foul and Pitt's Gibbs converted both free throws to put the game away.