The Red Raiders (18-10) were led by Mac McClung as the Georgetown transfer had 16 points while Kyler Edwards added 12 as the 2019 NCAA runner-up overcame a 26-23 halftime deficit.
Utah State (20-9) was paced by Justin Bean's 13 points while Neemas Queta added 11 with 13 rebounds and seven blocked shots and Marco Anthony also had 11.
Red Raiders use more efficient offense in second half to hold off Aggies
Texas Tech scored first on a jumper by Kevin McCullar and he hit a 3-pointer on the next trip down following an Edwards steal and assist for a 5-0 lead. Utah State went on a 10-0 run to lead 10-5 before a Marcus Santos-Silva layup and Burton jumper stopped it.
The Red Raiders led by seven after a 7-0 run that started with a Santos-Silva hook shot before a McClung triple and another Santos-Silva layup for a 19-12 lead with six minutes left in the first half before the Aggies went on another 10-0 run to lead 24-20 with 1:40 until the break.
Trailing 26-23 at halftime and down by six three minutes into the second half, Texas Tech went on an 8-0 run with Terrence Shannon Jr. scoring six of those eight points after he hadn't scored in the first half.
Edwards buried a three-pointer off an assist by Clarence Naldony to take a 36-31 lead with 14:24 remaining and McCullar hit another crucial three to push the lead to 41-33 to cap a 16-2 run. Micah Peavy scored on back-to-back baskets to give The Red Raiders a 45-35 lead, their largest lead of the contest.
McClung pushed the lead to 49-37 before Utah State scored a couple of baskets to stop the run and get the game back to single digits at 49-41. Edwards scored on a second-chance basket before a fast-break dunk by Peavy pushed it back to 55-41 with five minutes to play.
Utah State never found a rhythm offensively in the second half and Texas Tech moved on to the second round where they will face third seed Arkansas.
Texas Tech post-game quotes
Red Raiders coach Chris Beard, now 9-2 in the Tournament, described the game as "great NCAA Tournament games are a game of runs. We didn't want to get in a one-possession game with Utah State because we know how disciplined they are.
"They've got some really good players they can play through late. They did great this year through last-minute games. I thought specific to our successful run at the start of the second half, our defense remained consistent.
"The first half we guarded --- really what helped us on that run was our offense opened up. I told the guys, man, just take a deep breath here and be the best version of ourselves. We did get a little more aggressive offensively."