Baylor (14-6, 5-2 Big 12) trailed by 16 in the second half before twice cutting the deficit to one. Sooners freshman guard Buddy Hield spun and drove for a bank shot with 1:06 left, and Pledger made two free throws with 8.6 seconds left.
Romero Osby added 11 points for Oklahoma (14-5, 5-2).
Big 12 scoring leader Pierre Jackson had 22 points for Baylor, but missed a 3-pointer with 3 seconds left. Brady Heslip got the ball after the missed shot and stepped back, but his shot rattled off the rim as time ran out, though his foot might have been on the line anyway.
Isaiah Austin, Baylor's 7-foot-1 freshman, had 19 points and 20 rebounds.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.