The victory came in the quarterfinals of the Big 12 Tournament at Oklahoma City.
Texas faced a 43-25 halftime deficit, and its largest deficit was 48-28 with 17:05 remaining.
A.J. Abrams scored 16 points; Damion James and Craig Winder scored eight points each; Durant also had 13 rebounds and three blocked shots; and James added 11 rebounds and three blocks for the third-seeded Longhorns (23-8), who set a tournament record by winning after the largest deficit.
Curtis Jerrells led Baylor with 19 points and nine rebounds.
Mamadou Diene had 14 points and 12 rebounds; while Aaron Bruce and Henry Dugat each scored 12 points for the seventh-seeded Bears, who finished with a 15-16 record.
Baylor has lost its last 27 games against ranked opponents and has dropped 20 straight against Texas.