The Spartans completed a 13-1 season with their 10th consecutive victory in what was the 100th playing of college football's oldest bowl game.
Michigan State's Conor Cook threw for 332 yards and two touchdowns, putting the Spartans in front at 24-17 when he hit Tony Lippett with a 25-yard scoring pass with 13:22 to play.
Stanford drove the ball deep into Michigan State territory in the final five minutes, but had to settle for a field goal when Drone broke through from his defensive end position and threw Cardinal quarterback Kevin Hogan for an 8-yard loss on what had been a 2nd-and-8 play.
The Cardinal regained the ball for one last chance at a victory, but on fourth down at their own 34 and needing two yards to maintain possession, fullback Ryan Hewitt was overwhelmed at the line of scrimmage. The Michigan State defensive charge was led by Ellsworth, a linebacker who like Drone was playing his final game for the Spartans.
Stanford (11-3) took a 10-0 lead after one quarter, but could not manage another offensive touchdown the rest of the way. Its only other trip to the end zone came on a 40-yard interception return by Kevin Anderson in the second period.
Michigan State held Stanford to eight first downs and limited Hogan to 143 passing yards.
The win was only the second in six tries by the Big Ten Conference during the current bowl season. Ohio State will complete the league's bowl schedule when it plays Clemson in the Orange Bowl Friday.
The Pacific-12 Conference wound up its bowl campaign with a 6-3 record.