Nix put in 17 points and collected five rebounds. Payne contributed 14 points.
Branden Dawson also reached double figures with 12 points and six rebounds for the Spartans (14-3, 3-1 Big Ten), who notched their third straight victory.
The Cornhuskers (9-8, 0-4), meanwhile, remained winless in conference play despite 18 points and six boards from David Rivers.
Dylan Talley contributed 17 points and eight rebounds for Nebraska.