The 29-year-old Czech jumped on a loose puck at 4:40 in the extra session and scored for the Lightning, who tied the Stanley Cup series at 1-1.
Game three is set for Wednesday.
Blake Coleman scored twice and goalie Andrei Vasilevskiy made 22 saves for the Lightning in his 22nd playoff win — the most in franchise history ahead of Nikolai Khabibulin and Ben Bishop.
Coleman scored the most improbable goal of the NHL’s playoff quarantine bubble so far, crashing head first into the Boston goal.
He tied the game 1-1 halfway through the first period with a dynamic strike after finishing off a two-on-three rush with teammate Zach Bogosian. Bogosian split the Boston defence with the puck and, while falling, managed to somehow slip it over to Coleman, who timed his dive perfectly and tipped it past Bruin goalie Jaroslav Halak.
Brad Marchand put the Bruins ahead 2-1 with a late second-period power-play marker but Boston would fail to hold the lead.
Tampa was missing Ryan McDonagh, who sat out with an injury.
Not having McDonagh does not help the Lightning power play. The team won Tuesday despite going 0-2 on the power play after going 0-3 with the extra man in game one. They are now 0-15 on the power play in their last seven games.
Bruins goalie Halak lost for the first time in five games since taking over from starter Tuukka Rask who opted out of the Stanley Cup playoff bubble on August 15.
Elsewhere, Bo Horvat scored two goals while Tyler Toffoli and Elias Pettersson each had a goal and two assists as the Vancouver Canucks rebounded to beat the Vegas Golden Knights 5-2 in game two of their Western Conference series.
Jacob Markstrom stopped 38 shots and his defence set up a wall around him by blocking a team record 40 shots as Vancouver evened the series at 1-1.
Game 3 is Thursday.
Horvat now has eight playoff goals moving him into the postseason lead just ahead of Colorado’s Nathan MacKinnon and Dallas’ Joe Pavelski.
Tanner Pearson had an empty-net goal and Alexander Edler added a pair of assists for the Canucks.
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