Michigan (6-1, 2-1) lost for the first time under coach Brady Hoke. The Wolverines had a chance to tie it, but Robinson was sacked on fourth-and-1 from the Michigan State 9-yard line with 6:16 to play.
Robinson later threw an interception, and Isaiah Lewis returned it 39 yards for a touchdown with 4:31 left to make it 28-14. Shortly after that, Robinson was shaken up by a hit and left the game.
Edwin Baker ran for 167 yards and a touchdown for the Spartans.
Robinson ran for a first-quarter touchdown but was mostly ineffective through the air, going 9 for 24 for 123 yards and a touchdown on a windy day in East Lansing.
Down 21-7, Robinson found Roy Roundtree for a 34-yard touchdown with 9:49 left in the game. Martin then fumbled on an end around, giving Michigan the ball at the Michigan State 32.
After converting fourth-and-1 from the 23 with a short run, Robinson faced the same down and distance from the 9. Michigan called a slow-developing play-action attempt, and Johnny Adams sacked Robinson to end the drive.
After Michigan got the ball back, Robinson's pass was intercepted by Lewis, who took it back for a touchdown. Lewis risked a penalty by holding the ball out before crossing the goal line, but the touchdown stood.
Robinson's day ended a short while later when he was thrown down by Marcus Rush, who was called for roughing the passer. The Michigan quarterback stood on the sideline, grass stains all over his uniform, as the Spartans finished off another win over the Wolverines.
Michigan State hasn't had a four-game winning streak in the series since 1959-62 - which was part of a 6-0-2 stretch against Michigan.
With the game tied at 7, Michigan State went on a 54-yard drive to start the third quarter. On third-and-goal from the 10, Kirk Cousins found Martin, who caught the ball at the 5 near the right sideline and managed to stay in bounds before extending the ball across the goal line while being knocked backward toward the end zone.
Martin caught a 13-yard touchdown pass from Cousins in the final minute of the third, dodging a tackler and diving to that same front corner of the end zone.
Michigan State entered the game ranked No. 1 in the nation in total defense, and its defensive line gave Robinson problems all day.
Each team scored on its first possession of the game. Robinson gave Michigan a 7-0 lead with a 15-yard run, slipping away from Michigan State's Anthony Rashad White in the backfield and racing to the front corner of the end zone.
The Spartans answered with a 63-yard drive that ended with Baker's 1-yard scoring run.
The teams combined to punt four times from the defense's half of the field in the first half. One of those punts - by Michigan - came shortly after Devin Gardner had Stephen Hopkins open over the middle but threw incomplete toward the sideline instead.
Gardner went 3 of 7 for 45 yards for Michigan. He also came in after Robinson departed late in the fourth. With the Wolverines desperately trying to rally, Gardner had a touchdown pass called back because he was well past the line of scrimmage when he threw the ball.
On fourth-and-21 from the Michigan State 44, Gardner began running to the right sideline, then doubled back to the middle of the field, then circled back again to the same sideline before being stopped. Gardner had a receiver open deep down the field toward the end of the play but either couldn't see him or couldn't get rid of the ball.