The Blue Demons (5-7), who had the worst non-conference record among the 16 conference schools, opened an 18-8 lead on a 3-pointer by Cliff Clinkscales. They extended it to 40-25 with 14 seconds left in the half on Clarke's alley-oop dunk off an inbounds play from the baseline.
Corey Fisher made a 3-pointer with 3.2 seconds left in the half for Villanova (10-2) to make it 40-28 at halftime.
Burns hit a 3 to start an 11-2 run early in the second half that gave DePaul a 53-38 lead with 14:27 left.
Burns gave DePaul its biggest lead of the game when he made a steal and finished with a layup on the other end to make it 60-44 with 8:42 left.
Villanova then scored 10 straight points.
Dante Cunningham made a jumper then hit one free throw and Antonio Pena had a tip-in that got the Wildcats within 68-64 with 3:30 left. But Burns made two free throws and then had a steal and layup to put Depaul up 72-64 with 2:57 left.
Fisher led Villanova with 23 points and Cunningham had 16.
Villanova coach Jay Wright was called for a technical foul by official Tony Greene with 13:12 left in the first half for arguing a traveling call on Scottie Reynolds.
Will Walker, Clinkscales and Wes Green all had 12 points for DePaul, which lost at home to North Carolina A&T and Illinois-Chicago this season.
Reynolds, who came in averaging 17 points for Villanova, finished with 11.
Villanova was just 1-for-11 from 3-point range in the first half.
The Wildcats played without center Casiem Drummond. He missed his third game with a stress fracture in his right ankle and it hasn't been determined when he will return.