Marquette, trailing 59-58 inside the final minute, forced a turnover but Luke Fischer missed a contested layup and a tip didn't drop. Xavier pushed the ball upcourt and Bluiett was fouled, making two free throws at 15.7 seconds.
Matt Carlino, who had made 6 of 9 3-pointers, couldn't convert on a contested 3 with six seconds left and Bluiett's rebound led to the clinching free throw.
Xavier (12-6, 3-3 Big East) improved to 10-0 at home.
Carlino finished with 27 for the Golden Eagles (10-7, 2-3).
Marquette led 31-22 at the half behind Carlino's 10 points. A barrage of four 3-pointers in four minutes, the last by Abell who had five 3s, put Xavier ahead 47-45 with 7:20 left.