No. 4 Michigan 58, No. 10 Michigan State 57: Trey Burke recorded 21 points, including the go-ahead dunk off a steal with 20 seconds left, as the Wolverines edged the visiting Spartans to remain unbeaten at home. Burke, who also had eight assists, swiped the ball from Keith Appling and went in alone to give Michigan (24-5, 11-5 Big Ten) a 58-56 lead. Michigan State's Derrick Nix made one free throw with 8.8 seconds remaining and the Spartans had the ball with a chance to win before Burke made his fifth steal to end the game and Michigan improved to 17-0 at home.Adreian Payne had 17 points and 12 rebounds to lead the way for Michigan State (22-7, 11-5), which has lost three straight. Gary Harris added 16 points for the Spartans, who dropped two games behind Indiana in the Big Ten.Payne produced 12 points in the first half as Michigan State built its lead as high as seven before settling for a 31-28 advantage at intermission. Burke scored 11 on 4-of-5 shooting from the field and the Wolverines missed all six of their 3-point attempts in the opening 20 minutes.Michigan, which finished 0-for-12 from 3-point range, scored the first eight points of the second half and pushed its lead to 42-35 after two straight baskets by Mitch McGary (11 points). The Wolverines led by 10 with 4:36 left before Michigan State scored 14 of the next 18 points to tie it at 56 on a pair of Appling free throws.GAME NOTEBOOK: Michigan freshman G Nik Stauskas suffered a cut above his left eye in the first half that required stitches and did not return. … Burke has recorded the fourth 200-assist season in Michigan history. He has 201. … Michigan State beat Michigan 75-52 back on Feb. 12.