The Cowboys survived an upset bid in their first appearance since shocking Kansas last weekend.
It was the fourth straight win for Oklahoma State (16-5, 6-3 Big 12 Conference), which managed the victory despite shooting only 36 percent and hitting a mere 3-of-21 from long range.
Pierre Jackson hit two free throws with Baylor with 7 seconds left in regulation to force overtime and the Bears took the early lead in the extra period.
After the Cowboys came back to tie it, it appeared Baylor would take the lead again when A.J. Walton took a pass under the rim. His layup attempt, however, was blocked by Cobbins and Brown broke loose at the other end for a layup with two-tenths of a second remaining.
Marcus Smart led the Cowboys with 14 points and Brown had 13. Jackson led Baylor (14-8, 5-4) with 24 points.