Ryan Butler scored nine of his 10 points in the final two overtimes for the Spiders, who improved to 8-6 and won their fourth straight game. They also snapped a three-game losing streak against the Explorers.
Geriot hit 11-of-13 field goals but fouled out with 2:23 left in the first overtime.
The Explorers rallied from a 15-point deficit early in the second half despite going 12:40 without a field goal -- from 5:55 remaining in regulation until 3:15 left in the second overtime. They did hit 10-of-15 free throws to keep the game close.
La Salle's Terrell Williams missed an 18-foot jumper at the first overtime buzzer.
Butler scored all six of Richmond's points in the second extra session, but La Salle's Kyle Griffin tied the game at 68 on a 3-pointer with 53.3 seconds left.
The Explorers had another chance to win the game but Harris misfired on a 15-footer as time expired, forcing the third overtime. In that period, each team had the lead.
The Spiders went ahead 75-74 on a dunk by Gaston Moliva with 21.6 seconds left. La Salle still was left with two opportunities to win the game, but Green missed a shot in the lane.
The Explorers were awarded the ball after a jump ball was called, giving them one last shot on an alternate possession. Griffin misfired on a 3-pointer at the buzzer.
La Salle outrebounded Richmond 45-31.