Tied at 46 with 11 minutes to go, the Bears closed on a 24-14 spurt to win it by 10.
OU led by as much as seven in the first half when it was up 20-13 with 8:54 remaining in the opening 20 minutes.
Baylor came back to tie it and eventually take the lead late in the first half when guard Pierre Jackson hit a three to make it 31-29.
The Sooners, though, ended on a 5-0 run, all by guard Steven Pledger, to seize 34-31 advantage at intermission.
Both teams rode the seesaw to start the second half, trading the lead three times and tying six until the Bears commanded things down the stretch.
OU (14-14, 4-12 Big 12) finishes off the road portion of its slate when it heads to Austin for a 7 p.m. Wednesday battle against the Texas Longhorns.