The hard-serving 22-year-old from Thornhill, Ont., beat Belgium's Malisse 6-2, 6-1, 4-6, 6-4 in the match that was decided in just under two hours.
The 14th-seeded Raonic, who reached the third round a year ago, missed on a chance to serve it out leading 5-2 in the fourth set, but quickly won the match on his next chance as he finished with a 16th ace.
Raonic roared out to a fast start, winning the first two sets in just 44 minutes combined.
"I had my chances early on," he said. "I had a lot of deuce games and two break chances at the end. But I felt like I just let the grip go a little bit. He got into it (in the third set), he was playing well.
"I was settling a little bit too much in the rally points hitting backhands, whereas the first two sets I was trying really to find my forehand as much as I could."
Raonic converted on six of his nine break chances against the 54th-ranked Malisse and fired 61 winners.
The Canadian, who improved his French Open record to 3-2 with the win, awaits the winner of the match between France's Michael Llodra and Steve Darcis of Belgium.
Ivan Ljubicic was among the spectators for Sunday's win. The Croatian coach is working with Raonic "as a friend" on a trial basis through Paris after the player split this month with Spaniard Galo Blanco, Raonic's coach since late 2010.
Temperatures hovered around a chilly 10 C.
"It's better than the last few days, for sure, but it's pretty cold compared to the conditions I have played in the clay court season until now," Raonic said.
Eugenie Bouchard of Westmount, Que., Jesse Levine of Ottawa, and Vancouver's Vasek Pospisil all begin their French Open campaigns on Tuesday.