The 19th-seeded Thornhill, Ont., native, will face a true clay test in the next round when he plays Argentina's Juan Monaco after the 13th seed defeated Czech Lukas Rosol 7-6 (4), 6-0, 7-6 (5).
Raonic claimed his victory in just under two hours with 16 aces. The 21-year-old fired 40 winners and broke Levine five times.
A loser in the first round at Roland Garros last year, Raonic was able to dictate against his 131st-ranked opponent, letting Levine eventually make the errors.
Raonic is trying to extend a successful clay season after beating Andy Murray in the Barcelona quarter-finals last month before losing to David Ferrer in the semis.
Raonic saved six break points in victory, dominating in the final set against Levine as he ran away with it on an outside court. He advanced on his first match point as Levine put a return wide.
Raonic admitted the win was far from his best effort.
"The whole first set I struggled with my serve," he said. "Even after that I started getting it, but in glimpses. I wasn't serving consistently well throughout match."
Due to cooler temperatures of around 16 C, Raonic said he had to adjust his game.
"I wasn't getting as much kick on my second serve," he said. "He was stepping in when I was going to his backhand. But I wasn't getting enough behind the ball, I wasn't accelerating through it.
"I was trying to hit too much to his forehand side rather than just letting myself play. I started doing that in the third set more, just forgetting about everything and just focusing on myself."
The Canadian will be playing for the first time against Monaco, who owns six ATP clay titles, including two this season.
Both men will be bidding to reach the fourth round in Paris for the first time.
"(The preparation) is not really too different," said Raonic. "I've got to take care of my serve and play more forehands, not sit around and let the ball come to my backhand too much.
"I had a few opportunities today where I should have been running around a bit more. I need to do this, stay aggressive and try to control and dictate as much as possible."