Ramell Taylor and Jackson Stevenett scored 19 points apiece for the Thunderbirds (8-9, 3-4 Summit League), who shot 59.6 percent (28 of 47) from the floor en route to snapping a three-game losing streak.
Ian Chiles had 14 points and Stephen Thomas, Alex Young and Christian Siakam 10 each for the Jaguars (8-11, 2-5). Young scored his 2,000th career point, becoming the third player at the school and 11th in Summit League history to reach that total.
IUPUI led for only an eight-second stretch in the second half as Southern Utah kept a small but steady cushion for most of the game.
The Jaguars got within 61-58, but two Jones free throws and a Stevenett layup gave the Thunderbirds a seven-point advantage with 2:04 remaining. The margin got no fewer than five points afterward as Southern Utah protected its lead at the foul line.