Simmons also ran 17 times for 63 yards for the Coyotes (1-3). Kai Henry added 60 yards rushing on nine carries.
South Dakota opened the scoring in the second quarter on Simmons' 10-yard TD pass to Connor Herrmann.
Milo Hall's 5-yard run capped a seven-play, 80-yard drive in the third quarter for the Bears (0-4). Patrick Nassiat's extra point attempt was blocked and Northern Colorado trailed 7-6.
Ben Klett barreled into the end zone on a 12-yard run early in the fourth quarter to make it 14-6 for the Coyotes.
Jacob Knipp passed for 184 yards, Hall finished with 73 yards rushing on 20 carries and Jaren Mitchell caught four passes for 70 yards for the Bears.
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