Jerrell Williams had 12 points and Ruben Guillandeaux added 11 points and 8 assists for La Salle (14-10, 5-5 Atlantic 10), while Darrin Govens had 21 points and Ahmad Nivins 11 points and 14 rebounds for the Hawks (14-10, 7-3).
Nivins, whose 20 points per game leads the conference in scoring, was held to only three shot attempts in the game.
La Salle never trailed in the second half, and twice led by 10 points before the Hawks closed to 57-53 with 4:52 left. The Explorers then went on a 10-3 run, capped by a three-point play by Guillandeaux at the 1:27 mark, which helped seal the win.
The Hawks jumped out to an early 20-8 advantage, but La Salle responded with a 17-2 run helped by two 3-pointers by Green to lead 25-20. La Salle led 35-30 at the half, heading off 40 shots while making 15.
Saint Joseph's went 7 for 18 and committed 12 turnovers.