Matthews made it 4-2 at 9:44 with a snap shot from inside the left circle. He scored again on the power play at 12:29 with a tip off a shot from Nylander to make it 4-3.
"About halfway through the second period, we started to find our game a little bit and the ice started to shift a little bit even though we were down by three," Matthews said. "But the attitude and the mindset in the locker room was to just go out there and chip away."
Killorn gave Tampa Bay a 1-0 lead at 9:57 of the first period with a power-play goal off of a pass to the crease from Nikita Kucherov.
"This is a difficult one to process at the moment," Killorn said. "Having that lead and letting it slip away is tough, but we've got to get over it. They're a good team and their big-time players came through in a big way and I think we just sat back too much. We were a little too comfortable with that lead."
Sergachev made it 2-0 at 18:27 with a shot from the top of the left circle after a set-up pass from Kucherov.
Noel Acciari cut it to 2-1 at 4:51 of the second period with a redirection of a shot by Justin Holl that was going wide of the net.
"I hope that we look at this as a positive sign of the spirit of our team and what we can overcome," Maple Leafs coach Sheldon Keefe said. "I hope they take that and recognize that we have to keep pushing. The team we found a way to beat tonight, they are who they are because they very rarely lose two in a row, obviously don't lose three in a row very often and winning four in a row is going to be even harder. That's not lost on us."