Freshman Tristan Thompson had his second consecutive double-double with 11 points and 13 rebounds for the Longhorns, who also got coach Rick Barnes his 300th victory in 13 seasons at Texas. Barnes was already the winningest coach in program history.
A 14-2 run by Texas (6-1) to open the second half put the Longhorns ahead by 21 and opened up what had been a sloppy game by both teams in the first half when they combined for 25 turnovers.
Kendrick Harris scored 13 points for Lamar (4-3).
Jordan Hamilton scored 16 points and Gary Johnson had 10 for the Longhorns, but it was Joseph's timely shooting, rebounding and playmaking (four assists) that propelled the Texas offense in a sloppy game.
Texas missed 11 of its first 17 shots and trailed 11-5 early before Lamar started putting up wild shots and giving the ball away on turnovers. The Cardinals had 15 turnovers, almost half of them on traveling calls, and shot 25 percent in the first half.
Texas held Lamar scoreless for six minutes and took the lead on Hamilton's first 3-pointer. After making nine 3-pointers in the second half of Saturday's win over Rice, the Longhorns were 3 of 11 in the first half against Lamar. Joseph made two and the Longhorns led 34-25 at halftime.
Joseph's third 3-pointer sparked the Texas run to start the second half. Two more turnovers by Lamar, a three-point play by Dogus Balbay and a long jumper by Johnson put Texas ahead 48-27. Lamar got within 12 when Kendrick Harris' fast-break layup made it 56-44.
Jai Lucas then cut in for a reverse layup off a sharp pass from Hamilton and made a free throw for the Longhorns to end the Lamar run. Hamilton's 3-pointer with 4 minutes left put Texas ahead 69-49.