Jason Robertson, Sam Steel, Jamie Benn, Mavrik Bourque and Justin Hryckowian scored for the Stars (25-7-5).
Scott Laughton scored for the Maple Leafs (15-15-5), who lost their second of back-to-back games after a 5-3 loss to the Nashville Predators on Saturday and are 1-4-1 in their past six.
Jake Oettinger kept it 0-0 at 8:21 of the first period when he made a glove save on Auston Matthews’s breakaway.
The Stars went up 1-0 at 18:30 of the first period when Robertson got around Jake McCabe to retrieve a loose puck in the offensive zone and flipped a shot past Hildeby from the bottom of the right face-off circle.
Dallas appeared to stretch it to 2-0 at 8:22 of the second period but the goal was overturned after the Maple Leafs successfully challenged that the play was offside.
Toronto outshot Dallas 21-8 after the second period.
Steel made it 2-0 at 5:03 of the third period, scoring for the second-straight game, when he deflected a point shot from Ilya Lyubushkin in the slot.
Laughton cut it to 2-1 at 8:39 when he carried the puck on a 2-on-1 with Nicolas Roy and shot over Oettinger’s blocker from the left hashmarks.
The Stars went back up by two goals at 12:10 when Benn deflected a point shot from Miro Heiskanen in the slot to make it 3-1.
Bourque scored into an empty net at 17:55, ending a 10-game goal drought, to make it 4-1.
Justin Hryckowian put in rebound over Hildeby’s right pad at 19:43 for the 5-1 final.