In a matchup of No. 12 seeds, part of the expanded tournament's new look, the Tigers (22-11) went on a 21-2 run in the first half and never let the big lead slip away, as they had in several recent games.
Clemson hurried out after the game to catch a flight to a second-round game against fifth-seeded West Virginia (20-11) on Thursday afternoon in Tampa, Fla.
Milton Jennings added 11 points and Tanner Smith and Devin Booker each had 10 for Clemson, picked to finish seventh in the Atlantic Coast Conference.
Jamarr Sanders had 19 and Dexter Fields 12 for UAB, regular-season champions of Conference USA.
Ahead 39-27 at the break, Clemson never let the Blazers draw closer than eight points in the second half.
UAB's hopes wilted when, already trailing 61-42, it lost point guard Aaron Johnson to a right leg injury.
The Blazers didn't have a field goal for almost 81/2 minutes of the opening half and had more turnovers (eight) than points (seven) in the opening 10:30.