Hitting eight three-point shots made the difference for La Salle (17-8, 6-4) in the opening half. Guard Tyreek Duran netted a three just minutes in to help the Explorers to an early 7-2 edge. But with fewer than 12 minutes to play in the half, La Salle suddenly found itself in trouble when the Spiders closed the gap to one point.
With a 15-14 advantage, the Explorers fired back with five threes, including two each from Ramon Galloway and Sam Mills. La Salle extended its lead to 32-18 before Richmond answered with three treys of its own.
With fewer than five minutes to play, the Spiders were able to tie the game twice. But Galloway's perfect 2-of-2 shooting from the foul line with 5.2 seconds remaining sent the Explorers to the locker room with a 40-38 lead.
Richmond went up by four in the opening minutes of the second half. The game went bucket-for-bucket for most of the half, but the Spiders held La Salle at arm's length.
Duran netted back-to-back baskets, and Mills hit a three to return the lead to the Explorers. But La Salle couldn't manage to score again before Williams hit the game-winner for the Spiders.
Duran led the Explorers with 17 points. Mills had 16 points, and Galloway added 15. Forward Jerrell Wright contributed double-digit scoring with 11 points.
La Salle hit 70 percent of its free throws and went 10 of 17 from the three-point arc. The Explorers outshot Richmond, 46.4 percent to 39.3 percent.
Williams led all scorers with 22 points for the Spiders.