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.
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Maryland point guard Melo Trimble has withdrawn from the NBA draft and will return to College Park for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.