Texas Tech ended a streak of 32 consecutive losses to nationally ranked opponents over the last four seasons.
The Red Raiders (9-8, 1-3 Big 12 Conference) shot 57 percent from the field and held Baylor to 41 percent.
Crockett scored 19 points and was backed up by 17 points from Toddrick Gotcher and 14 each from Robert Turner and Dejan Kravid.
It was the first league win for Texas Tech under Tubby Smith, who is in his first year as coach of the team.
Kenny Chery scored 22 points for Baylor (13-3, 1-2 Big 12). The Bears have lost two of their last three.