Junior guard Craig Hannon led all scorers with 25 points, as he sank 7 of 14 shots from 3-point range and 8 of 15 overall from the field.
Senior guard Greg Rosatelli also had a big night as he scored 20 points on 7-of-9 shooting to go with a game-high five assists.
Other double-figure scorers for the Titans included senior guard/forward Dom Joseph with 14 points, freshman forward Ryne Murray with 12, and senior guard Nick Adams with 10.
Murray led the Titans with six rebounds, despite the Gators out-rebounding Westminster 39-27. Allegheny also held a slight shooting advantage as it out-shot the Titans 57.4 percent (35-61) to 53.7 percent (36-67).
Ryan Hollihan led the Gators with 24 points and 11 rebounds, while Casey McCloskey bucketed 22 points.
The Titans led by eight points (50-42) at the half before their lead swelled to 17 points (85-68) with 9:43 remaining in the game. Allegheny then mounted a comeback by cutting the Titan lead to four points (97-93) with 1:24 remaining. Rosatelli then made four straight foul shots to seal the win.
Westminster opens conference play Saturday when it hosts Washington & Jefferson at 6 p.m. in Presidents' Athletic Conference play.