Texas Tech overcame a 12-point deficit in the second half to take its first lead of the game on a free throw by David Tairu with 7:10 remaining.
But the Bears (11-3, 1-0 Big 12) toughened and used a 20-2 run to seal the win down the stretch. The Red Raiders (8-8, 0-1) went more than 4 minutes without a basket.
Dunn scored seven points in the run.
Jones, a freshman, tied his career scoring high. He made 8 of 9 baskets and was 4 of 6 from the line.
John Roberson scored 14 points to lead the Red Raiders. Tairu added 13, hitting hit 4 of 9 3-pointers.
After shooting no free throws in the first half, the Bears finished 12 of 15 from the line.
Down 41-29 after a 3-pointer by Dunn, the Red Raiders went on a 10-1 run. Mike Singletary got three points, Tairu hit a 3-pointer and D'walyn Roberts and Robert Lewandowski scored baskets.
After Tairu hit a free throw to give the Red Raiders the lead, Baylor used 11 free throws to keep the Bears ahead for good.
Baylor led 32-26 at halftime.
The Red Raiders hurt themselves in the first half, missing three of their first 12 shots and going on to commit 10 turnovers.
Jones started hot, scoring eight of the Bears' first 11 points.
The Red Raiders hit only 8 of 28 first-half shots, while Baylor went 14 of 32.
Free throws kept Texas Tech close. The Red Raiders were flawless on their six tries, whereas the Bears didn't shot a free throw.