Yves Mekongo Mbala had 17 points and Ruben Guillandeaux had 16 for the Explorers (11-13, 5-5 Atlantic 10), while Darrin Govens had a career-high 26 and Pat Calathes also 26 for Saint Joseph's (16-8, 7-4).
The second half saw eight lead changes and five ties until Saint Joseph's took an 81-75 lead with 6:06 remaining. The Explorers rallied to go ahead 83-81 and led 88-86 on a follow shot by Rodney Green at the 1:02 mark.
After a free throw by Garrett Williamson cut the lead to 88-87, Barrett's key shot was matched by Tasheed Carr's layup with 1:05 to go for the game's final points. The Hawks had one more chance with 0:01 left, but could not get a shot off.
Harris made five of 10 3-point attempts in the game to become La Salle's all-time leader in that department with 311.
