TAMPA -- John Tavares scored with 55 seconds left in overtime to lift the Toronto Maple Leafs to a 4-3 win against the Tampa Bay Lightning at Amalie Arena on Saturday.

Tavares punched in the puck past Lightning goalie Jonas Johansson off a pass from William Nylander, repeating his playoff heroics in this building 175 days earlier. Tavares scored in OT to give the Maple Leafs a 2-1 victory in Game 6 and a 4-2 series win in the best-of-7 Eastern Conference First Round, Toronto’s first playoff series win in 19 years.

"Good change by Auston [Matthews] and the puck turned over to us...just driving to the back post," Tavares said. "The group just staying together, staying with it. One shift at a time. Not trying to feel sorry for ourselves and not trying to look too far ahead. Just playing shift to shift. We stuck with it and found a way."

TOR@TBL: Tavares taps in pass in for OT winner

It was the first game between the teams since the playoff matchup, when Toronto won all three overtime games in that series.

"We're obviously frustrated," Lightning coach Jon Cooper said. "I've watched that movie before against these games. It's disappointing the way the players handled the third period, at least the last half of the third period, and overtime. We're much better than that."

Matthew Knies scored his first two NHL regular-season goals in the third period and had an assist for Toronto (3-2-0), which won for the first time in three games. Joseph Woll saved all 29 shots he faced after replacing Ilya Samsonov at 13:29 of the first period.

Samsonov allowed three goals on four shots.

"We stayed with it and I was happy to see our guys get rewarded," Maple Leafs coach Sheldon Keefe said. "Even in the first period I thought we played a good period. With their goalie playing the way that he was and Tampa playing as hard as they were you thought maybe time was going to run out for us, but it was nice to see the guys get rewarded."

Nikita Kucherov had two goals and an assist, and Johansson made 48 saves for the Lightning (2-2-2).

"Give Toronto a ton of credit, they did what you have to do to win hockey games," Cooper said. "They played the whole 60 minutes plus, and we didn't. And we left it on our goalie’s shoulders to bring it home, and that's so unfair.”

TOR@TBL: Nylander fires home a sweet pass

Nylander gave the Maple Leafs a 1-0 lead at 4:16 of the first period with a wrist shot from the bottom of the left circle off a pass by Tavares.

"This was a good test for our group, we stuck with it and found a way to win," Toronto center Max Domi said. "That was massive. [Woll] was great. He really reminds me of (Montreal Canadiens goalie) Carey Price's demeanor. He's very calm and relaxed on and off the ice. He's outstanding."

Kucherov tied it 1-1 with a power-play goal at 6:26 with a shot from the right circle.

Alex Barre-Boulet put the Lightning ahead 2-1 at 10:04 with a tap-in between Samsonov's pads off a pass from Kucherov.

"Maybe we were on our heels a little bit ... with a two-goal lead we've got to keep pressing," Barre-Boulet said. "The best defense is offense, we've got to keep forechecking."

Kucherov made it 3-1 with a power-play goal at 13:29, a slap shot from the top of the right circle that chased Samsonov. He already has three two-goal games this season, including two straight

"I thought we had good chances, but we just had a bad change there and gave them chances that they scored on," Lightning defenseman Mikhail Sergachev said. "[Johansson] was unbelievable and we as a team let him down."

Knies made it 3-2 at 12:11 of the third period when he beat Johansson to the top corner from the left circle. He tied it 3-3 at 14:33 with a tap-in from one knee to finish a 3-on-2 rush.

"It feels incredible, you know, it just feels awesome to get those to fall," Knies said. "[Domi] made some incredible passes. It feels really good to come out with a win. I think we got a lot of shots on net and tried to get the puck high."

TOR@TBL: Knies scores tying goal

NOTES: Keefe said that Woll will start Tuesday against the Washington Capitals and he's "pushing for more work." ... Kucherov had his 15th three-point period, second in Lightning history behind Martin St. Louis (16). ... Including the playoffs last season, seven of Knies' eight NHL points have come against the Lightning.