TAMPA, Fla. — Auston Matthews knows as well as anyone that Toronto‘s job is not finished.

The Maple Leafs took advantage of another late collapse by the Tampa Bay Lightning, moving to the brink of their first playoff series win in nearly two decades Monday night with a 5-4 overtime win in Game 4 of the best-of-seven matchup.

Toronto hasn’t won a playoff series since 2004 and has been ousted from the first round each of the past six postseasons, including a year ago when Tampa Bay rallied from 2-1 and 3-2 deficits to advance in seven games. Overall, since winning Game 7 of the 2004 conference quarterfinals against the Senators, the Maple Leafs have lost 10 straight playoff games with a chance to clinch a series.

“The fourth one is the hardest to get,” Matthews said after Alexander Kerfoot scored on the power play at 4:14 of overtime to give the Maple Leafs a 3-1 series lead.

“It’s feel different,” coach Sheldon Keefe said, though he also noted it’s important for the team not to get ahead of itself.

“We’ve got a tough task,” the coach added, looking ahead to Game 5 in Toronto on Thursday night.

The Lightning have won 11 of 12 playoff series over the past three postseasons, advancing to the Stanley Cup Final three straight years and winning the championship twice.

“We know what we’re up against, what they’ve accomplished” Matthews said.

Alex Killorn scored twice in helping the Lightning build a 4-1 lead that the Maple Leafs erased with three goals — two by Matthews — in a span of 6 minutes, 20 seconds. Morgan Rielly‘s second goal of the series tied it 4-all at 16:04 of the third period.

It was the second time in three nights Toronto rallied late to force overtime. Ryan O’Reilly‘s goal with 60 seconds left in regulation kept the Maple Leafs alive in Game 3, and O’Reilly won it at 19:45 of OT for a 2-1 series lead.

“We scored enough goals to win. You’ve got to keep them out of your net,” Lightning coach Jon Cooper said.

Mikhail Sergachev and Steven Stamkos also scored for the Lightning. Andrei Vasilevskiy stopped 32 shots and had a couple of big saves in overtime before Kerfoot redirected Mark Giordano past the goaltender for the win.

Noel Acciari scored for the second straight game for Toronto, deflecting Justin Holl‘s shot past Vasilevskiy early in the second period to briefly get the Maple Leafs within one goal before Tampa Bay pulled away with goals by Stamkos and Killorn that made it 4-1.

“Maybe there was a feeling that we’ll put it away,” Cooper said. “Obviously, Toronto had a different idea.”

It was 2-0 after one period, and the Maple Leafs were fortunate the deficit wasn’t bigger.

Goaltender Ilya Samsonov stopped Brandon Hagel‘s penalty shot a little less than eight minutes into the game, but the Lightning’s persistence paid off when Killorn — and then, Sergachev — scored their first goals of the series off perfect feeds from Nikita Kucherov.

In both cases, Samsonov was positioned to defend a possible shot from Kucherov when the Lightning star instead delivered the puck to Killorn and Sergachev from the right circle.

Killorn scored his first goal on a power play. His second came from on a shot from the left circle that beat Samsonov to the far post for a three-goal lead.

Samsonov stopped 27 shots.

Since winning the series opener on the road by four goals, the Lightning have lost three in a row heading into Game 5.

“You have to look at the big picture. We are still going to the rink,” Cooper said. “The series is not done yet.”

ESPN Stats & Information and The Associated Press contributed to this report.