A dunk by D.J. McCall gave IUPUI (5-10, 1-0 Summit League) a 43-29 lead with 15:29 left, but a 3-pointer by Joe Edwards sparked a 15-2 run - including eight points by Michael Calder - which cut the IPFW deficit to 45-44 with 9:15 to go.
Barksdale hit a pair of free throws to make it 56-48 with 3:38 remaining, but IUPUI went scoreless over the next 3-plus minutes and the Mastodons trailed by two, 56-54, with less than a minute to play.
After Barksdale broke the Jaguars drought with a three-point play, Max Landis answered with a 3 to make it 59-57 with 25 seconds left.
DavRon Williams and Barksdale made two free throws apiece from there to seal it.
Edwards scored a season-high 17 for IPFW (7-8, 0-2), which has lost six-straight games against Div. I opponents.