The Fighting Irish (3-0) snapped a six-game losing streak against ranked teams and beat a top-10 opponent for the first time in seven years.
The Spartans (2-1) had won 15 straight at home. The streak included a win over the Irish in 2010 on a fake field goal in overtime that preceded coach Mark Dantonio having a heart attack.
Notre Dame is off to its best start since 2002 when Tyrone Willingham won his first eight games as its coach. The Irish opened 0-2 last year and 1-3 the season before in Kelly's debut before bouncing back to finish with eight wins.
Coach Brian Kelly, though, is not ready to celebrate just yet with No. 17 Michigan (2-1) up next at home.
"There are a lot of things to work on," he said.
Michigan State had its worst showing on offense at home since losing 20-3 to Central Michigan in 1991.
Golson was 14 of 32 for 178 yards and a TD, a 36-yard pass to John Goodman. He ran for a 6-yard TD early in the second quarter to give Notre Dame a 14-0 lead.
"He made some big plays for us early which put us in a good position," Kelly said.
Andrew Maxwell was 23 of 45 for 187 yards and Le'Veon Bell had 77 yards rushing on 19 carries for the Spartans.
The Irish shook off a sloppy start that included George Atkinson running into a teammate on a kickoff return, a false start and a timeout before their first snap.
Golson missed an opportunity to connect with wide-open receiver Chris Brown on what would've been a TD, but the first-year starter made up for it with his arm and legs. On Notre Dame's second drive, Golson eluded a rush as he rolled to the right and threw back across the field on a 36-yard TD pass to Goodman for a 7-0 lead.
Maxwell threw a pass on the ensuing possession into the end zone that Bennie Fowler dropped in what proved to be the Spartans best shot to score more than a field goal.
Maxwell didn't have as much time to pass as he did in wins over Boise State and Central Michigan, and Bell couldn't run all over the Irish as he did in the opener against the Broncos. Maxwell was sacked three times in the second quarter alone - after not getting sacked in his first two games - and one of those hits behind the line forced a punt that gave Notre Dame good field position. Golson took advantage, scoring on a 6-yard run on a play that was designed to be a pass to cap a 51-yard drive and give the Irish a 14-0 lead early in the second quarter.
Michigan State responded with a 13-play drive that ended with Dan Conroy making a 50-yard field goal to match his career high and make it 14-3 late in the first half.
The third quarter included four punts for each team in the third quarter in a defense-controlled game that included eight punts for both teams.
The Spartans had a shot to force Notre Dame to punt early in the fourth, but Cierre Wood went left and cut back to the right on a 26-yard gain that seemed to deflate a team and crowd that didn't have much to cheer about all night.
Fans started to fill the aisles when Wood converted a fourth-and-1 from the Michigan State 37 with an 8-yard run to the outside. Kyle Brindza made a 29-yard field goal at the end of a time-consuming drive that took 6:21 off the clock and gave the Irish a 17-3 lead.
Michigan State's slim comeback hopes were dashed when Bell was going out of bounds and his lateral was caught by linebacker Manti Te'o with 4:20 left in the game to set up Brindza's 47-yard field goal that made it 20-3. Te'o had a game-high 12 tackles, one for a loss, and broke up two passes, playing just a few days after the deaths of his girlfriend, who had a long battle with leukemia, and his grandmother.
Notre Dame won its second straight in the series by more than a TD after nine of the previous 11 were closely contested contests.
Michigan State's defense gave up two TDs in the first half after not allowing one in the first two games. The unit improved as the game went on, but couldn't overcome offensive teammates that failed to move the ball consistently against Notre Dame's stingy defense.
The Spartans made their early appearance in the AP top 10 since 1979, but their lackluster showing will lead to them slipping in the rankings.
Notre Dame knocked off a top-10 team for the first time since Charlie Weis won his second game over Michigan in 2005.