Connor Brown put Toronto ahead on a short-handed breakaway midway through the third period, but Steen scored with goalie Carter Hutton pulled for an extra attacker by backhanding Alex Pieterangelo's rebound past Frederik Andersen.
Dunn snapped a low shot past Andersen after choosing to keep the puck on a 2-on-1.
Andersen stopped 40 shots and Hutton had 30 saves.
It was the Maple Leafs' first game back after the bye week. Their last game was a 4-3 loss to the Ottawa Senators on Jan. 10.
