Brenden Evans scored 10 for the Wolverines, Zach Nelson grabbed nine rebounds and Bruneel hauled in eight.
Tyler Larson led South Dakota with 13 points, Brandon Bos scored 12 and Tre Burnette grabbed nine rebounds.
The Coyotes out-rebounded the Wolverines 37-36, but shot 28.8 percent from the floor compared with 39.5 percent for Utah Valley State.
The Wolverines led 8-2 on free throws by Bruneel, but South Dakota tied it at 16 on a layup by Burnette. The Wolverines pulled away on an 8-0 run and led 31-23 at halftime.
South Dakota rallied in the second half on 3-pointers by Larson and Sekou Harris and trailed 44-42 at 4:09, but the Wolverines ripped a 5-1 run and Williams and Davis combined for seven down the stretch.