Olivier Labelle and Joakim Lindstrom each scored twice while Filip Novak and Ryan Caldwell added goals for the Crunch (11-21-1-2), who beat the Marlies for the second time in less than a week.
Erik Westrum replied for Toronto (14-18-2-3), which has lost four of its last five games.
Playing in front of an announced crowd of 3,128, the Marlies gave Syracuse a franchise-record seven power-play opportunities in the opening period. The Crunch capitalized almost immediately, putting two goals past goalie Jean-Francois Racine in less than 30 seconds, and finishing the frame up 3-0 on goals from Novak, Caldwell and Szwez.
Syracuse extended its lead at 4:23 of the second on Lindstrom's third of the year, before Westrum's 13th got the Marlies on the scoresheet at the 12:20 mark of the period.
Labelle, with two, Lindstrom and Szwez sealed the Crunch's victory with third-period goals.
Crunch goalie Tomas Popperle (8-11-1) stopped 19 shots, while Racine (6-9-3), who was pulled in favour of Todd Ford after the first period, made 14 saves.