Galloway scored 15 points and grabbed 10 boards for La Salle.
La Salle (16-6, 5-2 Atlantic 10) held a 66-59 lead before Duquesne scored seven unanswered to tie the game at 66-all with 1:23 left to play. But Galloway converted a three-point play and Sam Mills made two free throws to seal the win.
The Dukes (12-9, 3-4) won the battle of the boards 33-28 but shot just 41.4 percent (24 of 58) from the field while La Salle knocked down 51.9 percent (28 of 54) of their shots.
T.J. McConnell led Dusquesne with 19.
La Salle has won three consecutive games after losing two straight.