The Explorers (15-17), who will play No. 2 seed Temple on Friday, trailed by 14 in regulation and overcame a seven-point deficit with 1:22 left in the first overtime.
The Bonnies (16-14) led 71-67 with 3:04 remaining, then Jerrell Williams, who paced La Salle with 19 points, made a layup and Tyreek Duren's two free throws tied it with 2:32 left.
After Michael Davenport hit two foul shots to push St. Bonaventure ahead with 42 seconds to go, Weingarten hit his 3.
Ruben Guillandeaux added 18 points for the Explorers, including the tying shots in regulation and the first OT.
Andrew Nicholson's 30 points led the Bonnies.