Reynolds capped the game with a thunderous dunk from a Dee Davis off-the-backboard assist.
Davis tied a career-high with 15 assists for Xavier (15-9, 6-6 Big East) - his second double digit assist game of the season.
Xavier knocked down four consecutive 3-pointers, three by Myles Davis, to take a 50-44 lead early in the second half.
The Musketeers led by as many as 10 in the second half, until Providence crawled back within 60-58 following a 9-2 run and Ben Bentil tied it a 64-all with 6:33 left. But Xavier answered with a 10-0 run, eight from J.P. Macura.
LaDontae Henton led Providence (17-7, 7-4) with 24 points and nine rebounds.
Providence held a 40-34 lead at the break after six ties and 20 lead changes. Henton had 10 points and six rebounds.