The Bruins came back from a 16-point deficit to take a 62-60 lead with 5:32 to play on a jumper by Josh Shipp and then managed only two more points the rest of the way. UCLA missed eight of its last nine shots from the field along with its only free throw attempt.
UCLA's only basket during the final 5 minutes came from Alfred Aboya with 2:17 to go. It brought the Bruins to within a point.
Abrams made two free throws with 1:49 left to give the Longhorns a 67-64 lead and neither team could score until Abrams made one out of two foul shots with 10 seconds left.
Abrams led the Longhorns (6-1) with 31 points and Damion James had 13. No other Texas player managed more than six.
UCLA (4-2) was paced by Darren Collison with 22 points, but he made just nine of 22 attempts from the field.