"I don't think that they have a meter that could measure my happiness when (Sims) got out of the game," said Kentucky coach Matthew Mitchell, whose team got a congratulatory visit in the locker room from men's coach John Calipari. "We just couldn't stop her."
The teams combined for 80 fouls, 47 by the Lady Bears. The Wildcats were 49 of 66 on free throws, and Baylor was 33 of 46 from the line in just its third loss since the 2011 NCAA tournament. The Lady Bears have 81 wins in that span.
The Wildcats were coming off a 69-64 victory over No. 7 Louisville, which ousted Brittney Griner and then-No. 1 Baylor in the regional semifinals of the NCAA tournament last season.
Baylor won the only other meeting between the teams, 85-51 last season in Waco, 100 miles south of the Cowboys' home field.
Mackenzie Robertson, Mulkey's daughter, matched her career high with 23 points.
Janee Thompson scored 20 points for Kentucky, and DeNesha Stallworth had 16 points and nine rebounds.
O'Neill, who more than doubled her previous career high of 21 against Marist last December, missed a free throw to open the door for Imani Wright's tying 3-pointer in the final seconds of the first overtime.
Sune Agbuke did the same late in second OT for Baylor moments after blocking a layup attempt by O'Neill. Down two, Kentucky sent the game to a third overtime on a layup by Kastine Evans with 3 seconds left.
Thompson tied the third overtime with two free throws with 22 seconds left after the Wildcats missed three layups while down two points in the final minute. Robertson missed badly on a driving shot at the buzzer.