Sam Mills hit a 3-pointer to give La Salle a 76-74 lead with 1:13 to play before Williams tied it with a layup 18 seconds later.
La Salle turned the ball over with 21 seconds to go, setting up the heroics by Williams, who had 22 points and 11 rebounds. Darien Brothers added 13 points and Wayne Sparrow had 10 for the Spiders (13-12, 4-6 Atlantic 10 Conference), who snapped a three-game losing streak. It was their fourth straight series win.
Richmond had 45 rebounds to 27 by La Salle, and outscored the Explorers 16-2 on second-chance points.
Tyreek Duren scored 17 points, Mills added 16 and Ramon Galloway had 15 for the Explorers (17-8, 6-4), who have lost two straight by a total of six points.