Leading 76-72, the Explorers (6-3) made 8 of 12 free throws in the final 1:19 to hold off the Terriers (4-6), who closed to within a point on three occasions in the last 41 seconds.
D.J. Irving hit a free throw with 10 seconds left to make it 82-81, but missed the tying foul shot. Pettis hit his two free throws with 8 seconds left and BU's John Holland missed a 3-point attempt with 2 seconds to go.
La Salle trailed for most of the first half, falling behind 30-18 before closing to 38-35 at the break.
The lead changed nine times in the second half, with the Terriers holding their last advantage at 70-69 with 3:48 left.
Darryl Partin scored 20 points to lead BU, which shot 13 of 29 from beyond the arc.
Officials: North Carolina must show proof of discrimination-free zone, or lose NCAA tournament games
North Carolina must prove to the NCAA that its host arenas will provide a discrimination-free zone or risk losing NCAA tournament games in 2017 and 2018, multiple officials told ESPN.
Jalen Rose and David Jacoby examine the new NCAA draft rule and consider how it would have affected "The Fab Five."
Florida and Duke will meet on Dec. 6 in the Jimmy V Classic at Madison Square Garden as one of two high-profile games to help raise funds for cancer research.