Jordan Hamilton totaled 16 points and six boards while Tristan Thompson added 11 points and a game-high 13 rebounds for the Longhorns (6-1), who have won three straight.
Kendrick Harris had 13 points and Anthony Miles contributed 11 for the Cardinals (4-3), who had won their previous two.
The Cardinals had an 11-5 lead just over three minutes in when Miles buried a three-ball, but Texas responded to take over the game.
The Longhorns scored the next nine points and took the lead as Hamilton nailed a three-pointer.
Texas continued to extend its advantage and Joseph hit a three-pointer with under four minutes to play for a 27-19 lead, and the team took a 34-25 advantage into the break.
Texas ripped off 12 straight points early in the second half and extended its advantage to 48-27 on a Gary Johnson jumper less than two minutes in.
Lamar tried to keep in the game and got within 12 points thanks to Kendrick Harris’ layup with just over 10 minutes left, but Jai Lucas responded with a free throw and layup.
Texas’ margin never dipped below 12 points the rest of the way.
Texas has won all five matchups with Lamar. The last meeting was in 1995…Texas plays at USC on Sunday…Lamar plays at Rice on Saturday…The Cardinals shot just 25.7 percent while Texas made 45.3 percent of its shot. However, the Longhorns hit on just 23 of their 37 free throws.