Abrams hit eight 3-pointers and scored 26 points to help Texas beat Minnesota 76-62 in the first round of the East Regional on Thursday.
Damion James added 18 points and nine rebounds for the seventh-seeded Longhorns (23-11), who hit 11 of 20 3s overall to win their tournament opener for the fifth time in six seasons. Texas had lost seven of its last 14 games dating to late January.
Lawrence Westbrook scored 19 points for the 10th-seeded Golden Gophers (22-11), who were making their first tournament appearance since 2005. It was also Minnesota's first NCAA bid under Tubby Smith, who left Kentucky two seasons ago to rebuild the struggling Big Ten program.
Minnesota got off to its best start in more than 30 years at 16-1, but closed the year by losing 10 of 16.
The Gophers got the start they wanted, jumping to a 10-point lead in the opening 3 1/2 minutes, but the Longhorns hung around until Abrams found his range and turned the game into an impressive shooting display.
He finished 9-for-19 from the field and 8-for-15 from behind the arc, which was one shy of his career-high for made 3s. He missed three of his first four deep tries, but started finding his range late in the first half before getting free on a screen from Connor Atchley and burying a 3 just before the horn to make it 39-35 at halftime.
That turned out to be the first of six in a row, including a run of 3s on four straight possessions. After making the first two, Abrams fooled Blake Hoffarber into going airborne with a pump fake, then took a dribble to his right and coolly buried the 3 from right in front of the Texas bench. Then, after a pair of missed shots by Minnesota, Abrams took a pass and launched another one over Devron Bostick that swished cleanly through the net.
The last one pushed Texas' lead to 59-44 with 10:57 to play. Minnesota didn't get closer than 12 points the rest of the way.
Abrams' eight 3s were the most allowed by Minnesota all season, and followed a frustrating inability to defend the perimeter during the Gophers' late-season slide. It marked the ninth time in the last 16 games that Minnesota had allowed an opposing team to shoot at least 40 percent from behind the arc.
Dexter Pittman added 17 points and 11 rebounds for Texas, which shot 47 percent and took a 41-30 rebounding edge that led to 15 second-chance points.
Damian Johnson added 13 points for the Gophers, who shot 41 percent from the field.
For more postgame coverage from Burnt Orange Beat, read here.