With coach Kim Mulkey watching the game from her house while serving an NCAA suspension, the Lady Bears (30-4) advanced behind the big scoring games by the Big 12's top freshman and their most-experienced player.
Western Kentucky (24-9) led only once, but that was for less than a half-minute in the first half before Davis and Sims combined for all the Baylor points in a 14-4 run.
The only Baylor player ever with a 30-point game in the NCAA tournament had been Brittney Griner, who had five of them with a high of 40. It was the first time a pair of teammates had scored more than 30 points in an NCAA women's game since Gonzaga did it in 2011 according to STATS.
Baylor hadn't had two 30-pointer scorers since Danielle Crockrom and Sheila Lambert in a Big 12 game against Missouri on Feb. 18, 2001, during Mulkey's first season with the Lady Bears.
Mulkey served a one-game suspension for criticizing the officiating after the then-defending national champion Lady Bears' upset loss to Louisville in a very physical Sweet Sixteen game last March. Associate head coach Bill Brock filled in and is now 2-0 in his career when he's had to coach in Mulkey's place - he also did when Mulkey was ill during a regular-season game 10 years ago.
Davis made 11 of 13 field goals and 10 of 16 free throws. Sims, in her 14th NCAA tournament game, was 11-of-20 shooting with four 3-pointers.
The Lady Bears play Monday night against No. 7 seed California (22-9), which beat Fordham 64-63 in the earlier game Saturday at the Ferrell Center.
Chastity Gooch had 23 points for the Lady Toppers, and Sun Belt top freshman Kendall Noble had 21. Bianca McGee had 18 points that included four 3s.
Western Kentucky had its only lead after Gooch scored the first eight points in an 11-2 run. The Lady Toppers went ahead 28-27 on McGee's 3 with 6:43 left in the first half after Gooch had made a 3-pointer, a three-point play and a layup the previous 4 minutes.
But the Lady Bears responded with a 3-minute spurt led appropriately by Davis and Sims for a 41-32 lead that was their largest in the first half.
The Lady Toppers were in the NCAA tournament for the 17th time, but their first since 2008. They have been to three Final Fours.
They were 9-21 two years ago, but have now had 22 and 24 wins in their two seasons under coach and former WKU player Michelle Clarke-Heard.