Nick Cousins cut it to 3-2 at 11:43 when he took a pass from Aleksander Barkov in the slot and backhanded a shot over Murray's blocker in the slot.
Michael Bunting gave the Maple Leafs a 4-2 lead at 18:21 when he shot from the slot on a 5-on-3 man-advantage, the first such power play they've had this season.
"It's been a long wait, a long wait for one, that's for sure," Keefe said. "We're glad to get it. It didn't go in the way we drew it up but it's nice for the guys to come through. It was an important time in the game."
Alex Kerfoot made it 5-2 at 14:23 of the third period when Tavares centered a pass into the slot and Kerfoot shot between Bobrovsky's pads. It was his first goal since Jan. 17, ending a 25-game goal drought.
Marner scored short-handed into an empty net at 15:49 for the 6-2 final.
"The hardest part of it was we got into some penalty trouble and we had basically all the momentum," Tkachuk said. "[Defensive] zone, we didn't do a great job of shutting plays down, we kind of let them run all over the place and create their offense. They were moving around a lot, and we didn't do a good enough job of getting in front of Murray, he basically saw everything tonight. Just a tough one at a tough time of year.
"[The Maple Leafs] got crushed the other night by the [New York] Islanders (7-2 loss on Tuesday), they wanted to turn the page, and they turned it, and we didn't [after a 6-3 loss at the Philadelphia Flyers on Tuesday]."