It was the first road win of the season for the Blue Demons (3-1). The Panthers (4-2), who had won four straight, lost their home opener.
Both teams were looking to build early season momentum after finishing in last place last season in their respective conferences, DePaul in the Big East and Milwaukee in the Horizon.
The first half was tight, with neither team building a lead of more than four points. DePaul shot just 39.4 percent and Milwaukee just 33.3 percent.
The game was tied at 32 at halftime after Milwaukee forward Matt Tiby was fouled on a putback and made a free throw to convert a three-point play.
But Milwaukee was forced to call a timeout barely a minute into the second half after missing two threes and DePaul jumped to a 37-32 lead on a layup by Young and a 3-pointer by Melvin.
Milwaukee, which had won four straight -- including claiming the NIU Invitational over the weekend, defeating host Northern Illinois Sunday in the championship game in DeKalb -- seemed to run out of gas in the second half, playing their fourth game in five days.
DePaul, who beat Wright State of the Horizon League 81-72 on Saturday, gradually built a lead in the second half, going up 63-49 on a dunk by guard Charles McKinney with just over seven minutes remaining.
After the cold-shooting first half, DePaul shot 60.7 percent in the second period.
Milwaukee would get to within six, at 73-67 with just over a minute left when Tiby, who led Milwaukee with 20 points, made a layup.
But DePaul made its free throws down the stretch to prevail.
Melvin added nine rebounds to lead DePaul and Young had seven. Tiby paced Milwaukee with 11 boards.