Forwards Kris Kolanos, Matt Ellis and Kip Miller and defenceman Danny Syvret scored for the Griffins (2-0-1) in front of 3,105 fans at Ricoh Coliseum. Centre Matt Hussey chipped in with two assists.
Defenceman Marc Moro, who hadn't scored a goal since the 2004-05 season, and rookie right winger Jeff Corey replied for the Marlies (1-2-0).
Toronto goalie Jean-Francois Racine took the loss, making 24 saves on 28 shots.
The Griffins went 1-for-5 on the power play, while the Marlies were 1-for-6 with the man advantage.
Grand Rapids led 2-1 after the first period and 3-1 through 40 minutes.
The game was the first between Toronto and Grand Rapids since the two teams met in the first round of last spring's AHL playoffs. The Griffins eliminated the Marlies four games to one in the North Division semifinal series.
The Marlies' next game is at home against the Hershey Bears, the defending Calder Cup champions, on Sunday.