The 19-year-old won 78% of his first-service points and struck 24 winners in his 7-5, 6-0, 6-3 victory over Goffin to earn a place in the second round in Paris.
In the victory, which took just under two hours, Sinner won 11 straight games from 5-5 in the first set to a 3-0 lead in the third set.
“I never expected that,” said Sinner, when asked about the 11-game winning streak. “I was playing well from the beginning of the second set. I felt comfortable on court trying to go with the backhand a little bit more down the line and to open the court a little bit.”
The win was his second successive over Goffin, having beaten him at the ABN AMRO World Tennis Tournament in February.
Sinner, who is ranked world No.74, is the 2019 Next Gen ATP Finals champion. He was making his debut at Roland Garros. He made his Grand Slam debut at the Australian Open earlier this year.
But he showed no hint of any nerves on the big stage, breaking first to race into a 3-1 lead under the closed roof on the new Court Philippe-Chatrier.
“Obviously, it’s not easy playing against him,” Sinner said. “I know him quite well before, we practiced together quite a lot in Cincinnati, the US Open, Monaco. He’s a great guy. You go on court obviously to win.
“The first set was very tight, a lot of breaks of serve, and it was the key to manage to win the service games quite easily. In the beginning, that was not easy. He was returning well. I was not serving that well. But the balls here are very heavy. The court was heavy. It was not easy. But when you win the first set and go up a break, it’s a little bit easier to play. I mean, he’s a Top 15 player, so you always have to be focused. I tried to do that, and today it worked.”
Goffin, who was a quarterfinalist at the French Open in 2016, admitted “it was not a good match on my side.”
“It’s tough to lose a match like that, but he’s a great player. When I saw that I was playing against him first round, I knew it was going to be tough, especially in the first round when you have no rhythm. I didn’t have a win on the clay.”
Sinner will next face French qualifier Benjamin Bonzi who defeated Finland’s Emil Ruusuvuori.