On Michigan State's last possession, Keith Appling drove to the basket but had his shot blocked by Jordan Morgan. Brandon Wood of the Spartans came up with the ball, and Draymond Green was able to get another shot off from near the free throw line, but it missed.
Freshman Trey Burke scored 20 points for Michigan. He rebounded a miss by Appling in the final minute and turned it into a transition chance, eventually passing to Douglass for the winning layup.
Michigan (15-4, 5-2 Big Ten) has won three straight over Michigan State (15-4, 4-2).
Derrick Nix led Michigan State with 13 points.
After the final shot, Michigan State coach Tom Izzo tracked down the officials to discuss something, but after a brief conversation the officials headed off the court.
It was the first meeting between the in-state rivals with both teams ranked since 1998.