Betran put Austin Peay (2-1) up 70-68 with a jumper with 1:02 to play, then sank two free throws to hold off the Salukis. Chris Horton blocked Anthony Beane's jumper with 1 second to go to seal the win.
Betran scored 16 points for the Governors, including two 3-pointers, and Demarius Smith scored 12 points. Horton had a game-high seven blocks.
Austin Peay led 35-32 at halftime and led by as much as 17 points in the second period, but the Salukis closed, sparked by Jackson and Beane and a layup by Sean O'Brien that made it a two-point game with 13 seconds to play.