Bears guard Brady Heslip's wide open attempt at the buzzer was three-quarters of the way down before it rattled back out, allowing OU to hang on at the horn.
Before that, guard Pierre Jackson's attempt also went awry.
OU built a 15-point lead midway through the second half—it led 38-26 at intermission—but Baylor methodically battled back into it.
A 25-13 stretch allowed the Bears to close within two inside the final minute.
Sooner guards Je'lon Hornbeak and Steven Pledger, though, proceeded to hit 5-of-6 free throws, which allowed OU to maintain the lead it relinquished only one time in the contest, when Baylor led 4-2 in the early going.
The Sooners got up by as much as 14 in the first half behind 14 points from Pledger and another 12 from forward Amath M'Baye.
Both finished in double figures with 20 each.
Forward Romero Osby also bounced back with 11 points on 5-for-7 shooting, and he snared eight rebounds to go along with it.
For Baylor, four scorers finished in double figures, including star guard Jackson, who led all players with 22 points.
The Sooners improve to 14-5 overall and 5-2 in Big 12 pass, matching their conference win total from a year ago and drawing within one of their overall 2011-12 total.
They'll get back to action with a 5 p.m. CT Saturday showdown with No. 18 Kansas State inside Lloyd Noble Center.