Hagel tied it 2-2 at 19:28 of the first when his shot from the bottom of the right circle hit the stick of Maple Leafs defenseman TJ Brodie and deflected through Samsonov's legs.
Darren Raddysh put Tampa Bay ahead 3-2 at 13:34 of the second period. He skated around the net, shook off a hit from Jake McCabe and curled out in the left circle before scoring short side on Samsonov.
The Lightning had an opportunity to go up 4-2 at 15:41 of the second period when Brayden Point poked a loose puck past Samsonov, but the referee blew the whistle to stop play before the puck entered the net.
"It was probably the best game we played in this series. If we continue to play like that, I like our chances," Lightning captain Steven Stamkos said. "I thought we probably, not probably, I think we did deserve to win. But give them credit, they stuck with it. That's what really good hockey teams do, they find ways to win."
NOTES: O'Reilly is the second player in Maple Leafs history to factor into a game-tying goal in the final minute of regulation and the winner in overtime (Matthews, Game 4, 2020 Stanley Cup Qualifiers). … Marner is the fifth player in Maple Leafs history to start a postseason with at least three straight multipoint games (Darryl Sittler, seven games, 1976; Steve Thomas, three games, 1986; Miroslav Frycer, three games, 1983; Paul Henderson, three games, 1971). … Hedman played 32:35 after missing Game 2 with an undisclosed injury. … Tampa Bay defenseman Mikhail Sergachev played a game-high 37:27. … Lightning forward Tanner Jeannot had a game-high 11 hits.