Shelton went 6-for-7 from the field and 3-for-3 from the foul line, including a critical layup and two free throws in the final two minutes.
The Mustangs (3-2), who twice squandered 15-point leads in the second half, held off the Thunderbirds (1-3) down the stretch.
Geoff Payne led the Thunderbirds with 29 points, including 21 in the first half, and 12 rebounds. David Marek scored all 12 of his points in the second half and Tate Sorensen added 12 points and nine rebounds for Southern Utah.
Southern Utah won the rebound battle 36-33 but committed 20 turnovers and missed 15 free throws.
Payne kept the Thunderbirds close in the first half, hitting a layup with three seconds to go that cut Cal Poly's halftime lead to 33-29. But the Thunderbirds made only three field goals in the first 10 minutes of the second half and never could quite catch the Mustangs.