Gwen Jackson was the only double-figure scorer for Tennessee, finishing with 12 points. Kara Lawson added nine but hit just two of eight shots from the floor.
Tennessee led by nine points in the first half but Duke rallied to take a 36-31 lead by intermission. The second half was all Blue Devils. Tillis scored on a three-point play, nailed a 3-pointer and hit a 15-footer to spark the 17-3 run that built the lead to 53-34. Tennessee's only points during this stretch came on a free throw by Ashley Robinson and two more by Lawson.
Tasha Butts finally hit an inside bucket for Tennessee but freshman Jessica Foley answered with a 3 for Duke as the lead swelled to 20 points (56-36) with around 12 minutes left.
Gwen Jackson scored on a layup, a 3-pointer, two free throws and a drive as Tennessee pulled within 15 points at 66-51 but Beard scored twice inside to spark a 6-0 spurt that widened the gap to 72-51 with around 3:25 remaining.
Duke (2-0) built its biggest lead at 23 points (76-53) before Courtney McDaniel scored Tennessee's last two points on a pair of free throws with just over a minute remaining in the game.
Butts probably said it best: ''They fought hard; we didn't. They won; we lost. It's as simple as that. It shouldn't have been as hard as we made it.''
UT (1-1) hosts No. 22 George Washington on Tuesday night at 7 p.m.