Sandi Marcius added a career-high 19 points and 12 rebounds, while Billy Garrett added 14 for the Blue Demons, who had lost three of four. DePaul (5-4) also started a stretch of three games in seven days, which picks up Sunday when it hosts Chicago State and then Houston Baptist on Wednesday.
Melvin recovered from a rough outing last Friday against Arizona State, when he shot 2 of 12 for seven points in DePaul's 78-56 loss. On Thursday, he shot 7 for 13 for the Blue Demons, who were 32 of 61 (52.5 percent) as a team during their first game in six days.
Brandon Young, DePaul's leading scorer, was back in the lineup after missing last Friday's game with a sprained ankle and had 12. Marcius, a senior forward, topped the career high he set Dec. 1 against Oregon State when he scored 15 points on 6 of 6 shooting
Florida Atlantic (3-7) was led by Pablo Bertone's 30 points, and Jackson Trapp had 17. The Owls had won two straight over Central Florida and Jacksonville after six consecutive losses, but couldn't push their winning streak to three despite shooting 45.5 percent.
Bertone, the reigning Conference USA player of the week, hit 11 of 22 and couldn't help the Owls overcome a 38-29 rebounding deficit before fouling out with 11.7 seconds remaining.
Florida Atlantic was also looking for its first win somewhere other than its Boca Raton campus, but dropped to 0-7 away from home.
DePaul, meanwhile, is trying to reverse the program's decline but reached a milestone Thursday. A one-time power, the Blue Demons extended their all-time record to 1,400-905. They haven't been to the NCAA tournament since 2004, and aren't expected to contend for another this season out of the new-look Big East.
On Thursday, they overcame a slow first-half start but still managed to lead going into the break.
Florida Atlantic took an eight-point lead with 6:08 left in the half on a Bertone free throw, but the Blue Demons ended the period on a 17-8 run, capped off by Melvin's tip-in of his own layup to beat the buzzer.
DePaul took its first double-digit lead with 2:37 left on Garrett's 3-pointer, but the Owls got to within seven on a Bertone three-point play 21 seconds later. That, though, was as close as Florida Atlantic got.