Jackson scored six of Notre Dame's 10 points in overtime.
Denzel Valentine finished with 22 points and Branden Dawson had 16 points and a career-high 18 rebounds for Michigan State (5-3). After Valentine dribbled the ball off his foot to give it back to Notre Dame with 2.3 seconds left in regulation, Grant had a shot to win it on a drive to the hoop, but Valentine stripped the ball at the buzzer to send the game to overtime.
Valentine's 3-pointer with just more than two minutes to play tied it 64-all and stopped a 7-0 Irish run. Grant followed with a 3 on the next trip down the floor to get the lead back for Notre Dame, but Valentine answered with another 3 with 47 seconds left to tie it again at 67.
Jackson blocked Matt Costello's dunk attempt and then scored on a drive on the other end, and Grant grabbed a steal and converted a three-point play to give the Irish a 64-61 lead with 4:06 to go.
Dawson's baseline slam and a feed to Gavin Schilling for another jam with 10:31 left helped the Spartans build a seven-point lead while leading scorer Travis Trice was on the bench with three fouls.
After the Irish cut their deficit to one, Bryn Forbes knocked down a floater and Schilling came through with a three-point play to push the margin back to six with 7:41 left.
Trice came in averaging 16.4 points but finished with only seven on 3-of-13 shooting.
Consecutive 3-pointers by Grant and Steve Vasturia sparked a 10-0 run late in the first half to give the Irish a seven-point lead. Forbes hit a fallaway 3 with a second on the shot clock to end that spurt and scored the Spartans' final seven points of the half to cut Notre Dame's lead to 37-35 at the break.
The Irish played without V.J. Beachem, typically the first player off the bench, due to a right foot injury. Beachem is averaging 8.4 points and shooting a team-best 55.6 percent (15 of 27) from 3-point range.
TIP-INSMichigan State: This marked the Spartans' sixth game away from home out of their first eight this season. Their next seven will be played in East Lansing.
Notre Dame: It was Notre Dame's first game of the season against a Top 25 team. The Irish went 1-5 against ranked opponents last season.
-- Michigan State hosts Arkansas-Pine Bluff on Saturday.
-- Notre Dame hosts Fairleigh Dickinson on Saturday.