Melvin, a Baltimore native, reached double digits in scoring for the 26th consecutive game. He added eight rebounds.
The winning streak marks the longest for DePaul (9-3) since the Blue Demons won nine straight during the 1993-94 season.
For much of the second half, DePaul held a double-digit lead until six straight points by the Retrievers (2-10) cut the lead to four with 11 minutes to play. DePaul’s Moses Morgan then hit a jumper in the lane and added a free throw for a three-point play.
Jamee Crockett stole the ball and Brandon Young made two free throws, and Young found Melvin for an alley-oop to stretch the lead back to 11.
Aaron Morgan led UMBC with 15 points.