After trailing by as many as 18 points in the first half, Utah State had a chance to tie in the final seconds with a 3-pointer, but Butler stole a pass with 9 seconds left and streaked down the court to score and secure the victory for the fourth-seeded Mavericks (18-12).
On Friday, they'll face ninth-seeded UTSA, which upset top-seeded Louisiana Tech earlier Thursday.
“I think a lot of times you look at stats and they don’t necessarily tell the truth of the game, but tonight they really do," said Utah State head coach Stew Morrill. "They got 17 more shots than us, we shot a high percentage but we turned it over too much. There were lots of times when we got ahead but we couldn’t get stops."
Butler was 8 of 13 from the floor, including three 3-pointers. Karol Gruszecki added 17 points.
Jarred Shaw led the fifth-seeded Aggies (21-10) with 20 points, and Spencer Butterfield had 19.
Utah State fell behind in the first half 27-9 before rallying to cut the halftime deficit to 11.
"We were panicking at the beginning and we were not ready for the press," said Butterfield. "They were pressuring us hard, but once we got control of that we were able to break the press and do just fine.”
Texas-Arlington went ahead for good, 72-70, on Shaquille White-Miller's 3-pointer with 3:01 to play. Ben Clifford's 3-pointer with 40 seconds left pulled Utah State within 80-78 before a Butler free throw set up the closing sequence.
While its NCAA Tournament hopes are now over, Utah State could receive a bid to a postseason tournament, but Morrill does not think it's likely the Aggies would accept.
“I do not think we will be given the opportunity," said Morrill. "On the slight chance that we were invited, with all of our injuries our administration feels that we should shut it down.”