The Longhorns (3-0) will meet the winner of the game between No. 8 Notre Dame and Indiana in the semifinals on Tuesday.
Abrams was 4-for-7 from 3-point range, keeping his hot start from beyond the arc as he was 8-for-17 in Texas' first two games.
The Longhorns had allowed 44.5 points and 28.7 percent field goal shooting while forcing an average of 22 turnovers in their first two wins. No. 3 looked very familiar.
Ahmad Nivins had 14 points and 13 rebounds to lead the Hawks (1-2), who finished 17-for-58 from the field (29.3 percent), including 4-for-21 from 3-point range, and turned it over 18 times.
Saint Joseph's used a 6-2 run to close the first half to get within 37-28, but Damion James had seven points in Texas' 11-2 run to start the second half. Saint Joseph's missed three of its first four shots in the half and had three turnovers in the opening 1:40.
The Hawks scored seven straight points to make it 48-37, but they came up empty on their next eight possessions and Texas had its first 20-point lead, 57-37 on a layup by Gary Johnson with 8:55 to play.
James and Johnson both had 14 points for Texas. Johnson led the Longhorns with 10 rebounds.
Darrin Govens added 12 points for the Hawks.
This is the Longhorns' third appearance in Maui with their best finish a third in 2004.
The win gave coach Rick Barnes a 250-93 record in 11 seasons at Texas and he is 452-227 overall.