With the Musketeers leading 76-69 and less than a minute remaining, Dee Davis dished out the final of his career-high 15 assists on the day by throwing a pass off the glass for Reynolds on a fast-break.
The Friars were leading 40-34 at halftime before Xavier stormed back in the second half, outscoring Providence 44 to 29.
Reynolds came off the bench to score his 19, shooting 9-of-10 from the floor and adding seven rebounds. Musketeers forward Trevon Bluiett also poured in 19 points, while LaDontae Henton led the Friars with 24 points and nine rebounds.
Providence coach Ed Cooley left the game after dealing with an apparent stomach ailment and complaining of breathing issues and was transported to a local hospital.
Xavier improved to 15-9 (6-6 Big East), while Providence dropped to 17-7 (7-4 Big East).