The win keeps Idaho (12-14, 7-8 Big Sky Conference) in the hunt for post-season tournament play.
Down by five after Callandret's free throws, Jordan Gregory drew Montana within 89-86 with two free throws with 23.6 seconds left, but Idaho's Bira Seck hit a free throw, then Sekou Wiggs added two more.
Gregory scored a career-high 36 for Montana (16-11, 12-4). Mario Dunn added 11.
Gregory's 24-foot 3-pointer with 9.3 seconds left in OT tied it at 70 to send the game into double overtime.
Leading 33-24 at halftime, Montana was up by nine with two minutes left in regulation when Idaho rallied and Scott tied it at 58 with two free throws.