The sensational freshman had 17 points, 10 rebounds and seven blocked shots Friday, and the Longhorns survived a second-half comeback by high-scoring Oakland for an 85-81 victory.
Thompson controlled his head-to-head matchup with Summit League Player of the Year Keith Benson while getting plenty of help from frontcourt partner Jordan Hamilton, who finished with 19 points and 10 rebounds in an impressive one-two punch.
The No. 4 seed Longhorns (28-7) led by 15 with less than 5 minutes remaining, but the Golden Grizzlies cut the lead to 80-75 with 1:23 left. Texas then hit five free throws in the final minute to advance into a third-round matchup with Memphis or Arizona in the West Regional.
The Longhorns took care of business a day after fellow No. 4 seed Louisville lost to Morehead State. Texas fell in the opening round to Wake Forest last year.
Reggie Hamilton scored 25 to lead Oakland (25-10). Benson had 14 points and 11 rebounds.
The 6-foot-8 Thompson was up for the challenge of battling the 6-foot-11 Benson in the first half. The freshman grabbed three offensive rebounds on the Longhorns' first three possessions while battling head-to-head with the senior big man.
Oakland had no answer at times for Thompson, who grabbed his own alley-oop miss for a putback early in the game. He followed that with an inside spin move against Benson for a basket that put Texas up 10-7 in the first few minutes.
Thompson was equally effective on defense, blocking Benson twice in the opening half and limiting him to six points. Thompson had nine points, four rebounds and four blocks by halftime.
Texas led by as many as 12 in the first half, taking a 33-21 lead after Jordan Hamilton made an inside cut and took a pass from Gary Johnson for a layup.
The Golden Grizzlies responded to their biggest deficit with a 7-0 run that cut the lead to 33-28. Hamilton and Will Hudson each had putbacks, two of seven first-half offensive rebounds for Oakland, and Travis Bader had a 3-pointer during the run.
Jai Lucas' 3-pointer gave the Longhorns their largest lead of the game at 63-46. Texas led 78-63 after a jumper by J'Covan Brown with 4:58 remaining, but the NCAA's second-highest scoring team refused to fold. Larry Wright hit a 3-pointer with 1:23 remaining to close within 80-75.
Texas hit five free throws in the final minute to secure the win. Brown hit two of the final free throws, finishing 12 of 12 from the line and with team-high 21 points.