Epke Udoh, the Big 12's newcomer of the year, scored 25 points for the third-seeded Bears (25-6), who will meet No. 2 seed Kansas State in the semis.
Damion James had 18 points and 12 rebounds for his second straight double-double for Texas (24-9) but the all-conference senior drew one of Texas' two technicals and fouled out with 2:43 left. A few seconds later, center Dexter Pittman also fouled out for Texas, which started the season 17-0 and climbed to No. 1 before falling out of the rankings.
Tweety Carter had 20 points for Baylor, which hadn't beaten Texas three in a row since 1981-82.
Dunn, benched with two points just 4 minutes, 20 seconds into the game with three fouls, scored seven points in a 13-2 run that put Baylor in command at the beginning of the second half.
Pittman's basket got the Longhorns to 43-41 in the first seconds of the second half, then Udoh scored, Dunn followed with a driving layup and Udoh came right back with another basket.
Dunn, fouled by James, sank a free throw and then followed with another basket and then another foul shot when James was whistled for a technical foul.
After Carter stole a Texas pass and drove in for a layup, the Bears led 56-41.
Pittman, the Longhorns' bulky senior center, scored six straight points and cut the lead to 64-59 before Dunn answered with a 10-footer and Carter followed with a running one-handed basket.
Dunn, with an assist from Carter, went in for a layup and made the foul shot when Pittman picked up his fourth foul, putting Baylor up 71-61.
Pittman and Avery Bradley each had 14 points for the Longhorns.
James, who had 28 points and 16 rebounds on Wednesday against Iowa State, picked up right where he left off, putting in 16 points and grabbing seven rebounds in the first half.
Baylor managed to take a 43-39 lead into halftime in spite of getting only two points from Dunn. The Big 12's second-leading scorer with almost 20 points a game, went to the bench with his third foul after he and Texas' J'Covan Brown each drew a technical foul.
Players on each team began taunting each other and officials acted quickly before things got out of hand between the two rivals who were playing for the 234th time.