The Cowboys pulled away after owning only a one-point halftime lead and bounced back from their 74-71 loss to Kansas State that opened Big 12 Conference action.
Brown made 8-of-13 to score 27 points while Smart had 11 rebounds to go along with his 24 points. Smart went 16-of-20 from the foul line.
Phil Forte came off the bench to score 14 points for the Cowboys (13-2, 1-1 Big 12), winners over Texas in each of their last four meetings.
Texas had won six in a row, but has now dropped three of four. Demarcus Holland and Demarcus Croaker both had 12 points for Texas (11-4, 0-2 Big 12).