The Dukes (17-7, 9-2) were led by Bill Clark with 16 points, six rebounds, seven assists, two blocks and one steal.
T.J. McConnell added 15 points, Damian Saunders 14, Mike Talley 13 and B.J. Monteiro 12 for the Dukes. Saunders also had 13 rebounds and five steals. McConnell added four blocks and five steals.
The Dukes jumped out to a 32-10 lead, but the Minutemen closed to 38-25 at halftime.
UMass got within nine points of Duquesne with 13 minutes to go, but Clark responded with a three-pointer and a dunk to push the lead back to double digits.
Duquesne has won 12 of their last 14 games. They will now go on the road to face Dayton on Saturday.