Jarrett Allen's last-second shot for Texas rolled off the rim.
Andrew Jones, who led the Longhorns with 16 points, hit a 3-pointer with 1:20 remaining to cut Georgia's lead to 57-56. Maten answered with a layup before Eric Davis Jr. made one of two free throws, leaving the lead at 59-57.
Georgia's Derek Ogbeide's put-back of a miss by Frazier appeared to push the lead to four points. Following a review of the play, officials ruled the shot clock expired before Ogbeide's shot, leaving the Longhorns with the ball and 8.9 seconds.
Allen missed a short jumper as time expired.
Georgia (13-8) snapped a streak of two straight losses. Texas (8-13) has lost six of seven.
Frazier scored 11 of his 14 points in the second half. He missed each of his five shots from the field in the first 20 minutes before helping Georgia rally from two 10-point deficits.
The Bulldogs made only 7 of 24 shots (29.2 percent) in the first half, including 0-for-6 shooting on 3-pointers. The Longhorns made 5 of 14 3s in the half. A 3-pointer by Davis gave Texas its first double-digit lead at 19-9.
Georgia closed the deficit to 22-21 before Texas closed the half with a 10-2 run to lead 32-23 at halftime.
Frazier's first two field goals of the game helped the Bulldogs score the first eight points of the second half. Georgia's first 3-pointer of the game by freshman Jordan Harris gave the Bulldogs a 38-36 lead -- their first advantage since 8-7. Georgia missed each of its eight 3s before Harris ended the drought.