Brown had three 3-pointers and was 6 of 6 from the free-throw line. Sheldon McClellan added 19 points in his first start and the Longhorns (10-3) won in their first game since losing at No. 5 North Carolina on Dec. 21.
Rice missed five layups and shot 29 percent in the first half but only trailed 35-27 at intermission. The Owls (9-5) got within one point in the second half before Texas used a late run to seal the win.
Tamir Jackson had 19 points but Rice missed the chance to beat a second Big 12 team in two weeks after winning at Texas A&M on Dec. 22.
Julien Lewis did not play after starting 12 straight games for Texas. The freshman guard injured his left hand on Thursday when it got caught in a car door.