Jesse Schultz, Jannik Hansen and Brad Moran also scored for the Moose (1-1-1-0), who took a three-goal lead in the first period and never looked back.
Robbie Earl and Erik Westrum replied for the Marlies (1-1-0-0), who trounced Syracuse 6-0 in their season opener Friday.
Playing in front of an announced crowd of 3,650 at Ricoh Coliseum, Manitoba opened the scoring at 8:20 of the first period when Schultz capitalized on a 2-on-1 break for his second goal of the season.
Hansen made it 2-0 at 11:08, just as a two-man Manitoba power play was expiring. Jaffray added another extra-man marker at 17:27.
Toronto got on the scoreboard at 5:02 of the second on the first pro goal of Earl's career. But seven seconds after Marlies winger Martin Sagat took an interference penalty, Moran restored Manitoba's three-goal lead at 13:36.
Westrum scored with 44 seconds remaining in the second period to cut Manitoba's lead to two, but Jaffray's second goal of the night at 9:49 of the third put the game out of reach.
Marlies goaltender Justin Pogge, making his pro debut, stopped 25 shots in the loss. Manitoba's Drew MacIntyre made 30 saves for his first win of the