The Sooners (22-9) will play archrival Oklahoma State in a semifinal on Saturday.
Stevenson's 3-pointer with 4:16 left to put the Sooners up 50-49, and she hit another 3 and made a layup to keep her team ahead in the final minutes.
Griner, suspended two games for punching a Texas Tech player March 3, had 13 points and set a tournament record with 10 blocks for defending champion Baylor (23-9).
Morghan Medlock led Baylor with 18 points and Shanay Washington had 12.
Amanda Thompson had 15 points, eight rebounds and four steals for the Sooners.
Baylor's Melissa Jones missed a 3-pointer that would have tied it with 6 seconds left, and Oklahoma's Abi Olajuwon came down with her 10th rebound, got fouled and made the free throws.
The NCAA suspended the 6-foot-8 Griner for one game, and coach Kim Mulkey added an additional one, after Griner punched and broke the nose of Texas Tech's Jordan Barncastle.
Prior to that incident, Griner was best known as a YouTube sensation for her dunking ability and the dominance she's shown in her first season at the college level.
She made first-team All-Big 12 and was named the conference's freshman of the year after averaging 19 points, 8.7 rebounds and six blocked shots.
The Bears struggled in her absence, losing 70-54 to Texas in their final regular-season game and getting extended to the last minute before putting away 11th-seeded Colorado 72-65 on Thursday.
Griner was at her best against Oklahoma during the regular season. She had 12 points, nine rebounds and 11 blocks in a 57-47 win and 17 points, 12 rebounds and 11 blocks in a 62-60 overtime loss.
Griner received a smattering of boos from Oklahoma fans during pregame introductions.
The Sooners tried to deny the ball to Griner, with Olajuwon and Joanna McFarland taking turns defending her with help from teammates. Olajuwon and McFarland had four fouls each by the middle of the second half.
Griner was 4 of 10 from the field, had six rebounds and passed for two assists.