Jerrell Wright, Ramon Galloway and Tyreek Duren added 15 points apiece for the Explorers, who ended a three-game skid.
Trailing 15-5 early, La Salle (18-9, 7-5 Atlantic 10 Conference) built a six-point lead before Massachusetts (18-8, 7-5) knotted the score at 33 at halftime.
After the Explorers pulled ahead 60-51 with 6:08 remaining, the Minutemen used a 12-2 run to lead 63-62 with 3:54 left, with Maxie Esho scoring seven of his 18 points.
Tied again at 66, Duren hit a jumper and he and Pettis made one free throw apiece for a 70-66 lead with 21 seconds remaining.
Esho's three-point play with 13 seconds left again made it a one-point game, then Duren answered 3 seconds later with two free throws.