Prince was 9 for 14 from the field, including three 3-pointers. He didn't score in the second half until 8:32 remained.
Lester Medford scored 10 points for the Bears (19-7, 7-6 Big 12).
Royce O'Neale hit a 3-pointer with 4:08 to go to put the Bears up 48-43 after the Red Raiders pulled within two points on a dunk by Keenan Evans.
A 3-pointer by Devaungntah Williams with 13 seconds remaining pull the Red Raiders to 52-49 but they got no closer.
Texas Tech scored 16 points off of 16 turnovers by Baylor and outscored the Bears 12-4 on second-chance points.
Williams scored 15 points and Zach Smith added 10 to lead Texas Tech (12-15, 2-12).