Gibbs started the winning run with a layup that tied the game at 75 with 4:12 left. He added two free throws after a turnover and Whitehead contributed four free throws, making it 82-75 with 2:38 left.
Gibbs, who also had eight assists, made four free throws in the last minute to finish 8-8 from the line for the Pirates (15-6, 5-4 Big East). Desi Rodriguez added 16 points.
The Pirates had had lost three straight and four of five, starting with a loss at Xavier when they were ranked 19th. Whitehead, a freshman who had started the first 11 games, had missed the last nine with a stress fracture in his foot.
Trevon Bluiett had 19 points and Jalen Reynolds 17 for the Musketeers (14-8, 5-5), who were coming off a win over No. 21 Georgetown.