A pair of Michigan State false start penalties that cost the Spartans 10 yards and about 15 seconds as the first half wound down, saved a 7-point tie for Notre Dame entering the break.
The Spartans had pushed their way to the Irish's 34-yard line with 47 seconds to play when back-to-back false starts moved them back to the 44 with 32 seconds left in the half.
Michigan State then had three incomplete passes, punted the ball out of the end zone and Notre Dame took a knee to end the opening half.
Michigan State tied the game when quarterback Kirk Cousins hit Keshawn Martin for a 6-yard touchdown to cap a seven-play, 94-yard drive.
The scoring drive was started after Johnny Adams' picked off a Dayne Crist pass intended for Theo Riddick at the Spartans' 6.
Notre Dame escaped Michigan State's first scoring threat at the start of the second quarter
The Spartans drove to the Irish 8-yard line on a drive the spanned the first two quarters, but Michigan State quarterback Kirk Cousins' pass was tipped by cornerback Robert Blanton and safety Zeke Motta picked it off in the end zone.
Notre Dame gave the ball back on the ensuing drive.
Irish receiver Michael Floyd had the ball stripped by a Michigan State defender. The throw was initially ruled incomplete, but a review showed the Spartans' Chris Norman knocked the ball away from Floyd and Marcus Hyde recovered it at the 11.
Notre Dame forced a three-and-out and had the ball on the Spartans' 27 after former Bishop Dwenger star John Goodman's 4-yard punt return, but Adams came up with the pick to start Michigan State's scoring drive.
Crist is 14 for 28 for 158 yards with a touchdown and an interception, and Cousins has completed 11 of 21 for 116 with a TD and INT.
Armando Allen, who ABC reported hurt his hand in the second quarter, has 31 rushing yards, while Michigan State's Le'Veon Bell has run for 77 yards with a pair of 16-yard gains to his credit.