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.