Marcellus Barksdale scored from distance and Khufu Najee converted two at the line to edge the Jaguars within two points, 57-55, with 2:42 left to play. South Dakota State (18-8, 9-3 Summit) had led by eight just under two minutes earlier, but went 3:30 without a field goal.
Bittle finished with 13 points, four assists and four steals. Marshall had eight of the Jackrabbits' 22 rebounds.
IUPUI (8-16, 4-6) committed 20 turnovers by games end, which led to 21 SDSU points. Barksdale scored 10 points - all in the second half - and grabbed 10 boards.