Melvin scored 24 first-half points—including 13 points in the opening 4 minutes—as DePaul (3-3) snapped a two-game losing streak.
Derek Needham paced Fairfield (3-4) with a career-high 29 points.
The Blue Demons quickly pushed their lead to 16 points early in the second half, then held off a late Stags rally capped by a Needham 3-pointer that cut the lead to 78-73 with 2:03 left in regulation.
Charles McKinney and Donnavan Kirk had 11 and 10 points, respectively, for the Blue Demons. Amadou Sidibe had 11 points and a game-high 11 rebounds for Fairfield.