Rhodes scored 14 points, J.T. Miller had 13 and Scurry 11 for Missouri State (9-3).
Turnovers have been a problem for Missouri (8-2) early in the season, but it only had eight against Green Bay.
The victory is the first for the Razorbacks (7-2) over a top 15 team since defeating No. 5 Texas A&M during the 2015-16 season.