Rodney Green had 14 points to lead four players in double figures for the Explorers (14-12, 5-7), who dropped their second straight.
The victory guarantees Duquesne its second straight winning season, marking the first time since the 1979-80 and 1980-81 seasons they will finish above .500 in two straight campaigns.
Jackson got Duquesne off to a strong start, making seven of his first nine shots to finish with 17 points in the first half and help the Dukes to a 44-41 lead at the break. Vernon Goodridge's layup 13 seconds into the second half brought La Salle within 44-43. But the Dukes scored the next six points and the Explorers never got closer than three the rest of the way.
Eric Evans also reached double figures for Duquesne with 11 points, while Saunders set a career high with 14 rebounds. Kimmani Barrett and Paul Johnson had 12 points apiece for La Salle, and Goodridge finished with 11.
