Toronto built a 2-0 lead through one period and although the Flames twice moved within one they could not overcome their deficit.
It was the third straight victory for the Maple Leafs, who became the first team in the Eastern Conference to win 10 games.
Van Riemsdyk's goal was the critical score of the contest, coming shorthanded with just four seconds left in the first period.
Toronto had a 2-1 lead heading into the third, an advantage that grew when Mason Raymond scored 5:59 into the period. David Jones cut the lead in half with 5:21 to play, but Paul Rangers produced another shorthanded goal into an empty net to wrap up the victory.