Texas established dominance quickly, jumping out to 9-0 lead in the game's opening four minutes. The Longhorns led 39-24 at halftime and the lead ballooned to 70-42 with 6:28 left.
Abrams sank 10 of 16 shots, including 6 of 10 three-pointers. Reserve Dexter Pittman scored 11 points with 10 rebounds.
Damion James had 10 points and 10 rebounds, while Connor Atchley added 12 points with seven rebounds and three blocked shots for the second-seeded Longhorns (29-6), who won the battle of the boards 40-32 and limited Austin Peay to just 28.8 percent shooting.
The losers were led by Ernest Fields' 14 points and nine rebounds. Todd Babington had 11 points and five rebounds for the 15th-seeded Governors (24-11), whose last NCAA Tournament win was a 90-87 victory against Providence in 1987.