Ben Ondrus, Jay Harrison and Robbie Earl scored for the Marlies (23-29-2-4) in front of an announced crowd of 4,416 at Ricoh Coliseum. The Marlies have won two of their last three games.
Rochester (36-20-1-0) has lost four in a row.
Toronto opened the scoring on Ondrus' short-handed goal of the first period, a period in which the Americans could manage only two shots on Pogge.
The Marlies extended their lead when Harrison's slapshot from the point that made its way through traffic and past goalie Adam Dennis at 11:13 of the second period.
The Marlies didn't get a shot on Dennis until nearly the 15-minute mark of the third, but Earl's seventh of the season into an empty net at 19:43 sealed the victory.
The Americans were unable to score on any of their 10 power-play opportunities, while the Marlies were 0-for-4 with the man advantage.
Dennis made 31 saves for Rochester.