The Tampa Bay Lighting can book their flight to Edmonton.
Anthony Cirelli and Ondrej Palat scored in regulation for the Lightning, while Andrei Vasilevskiy stopped 45 shots inside an empty Scotiabank Arena. Hedman and Kevin Shattenkirk finished with two assists apiece.
David Krejci, with a goal and an assist, and David Pastrnak replied for the Bruins. Jaroslav Halak made 32 saves.
On the winner, Hedman’s shot from the left circle got past Halak to send the Lightning streaming off the bench in celebration.
Tampa, which is in the conference final for the fourth time in the last six years, now heads to Alberta’s capital as the first team to qualify for the third round of the NHL’s pandemic-halted season.
The Lightning will take on the winner of the East’s other semifinal between the New York Islanders and Philadelphia Flyers. The Islanders lead that best-of-seven series 3-1 and can clinch Tuesday night.
The Stanley Cup final will also be played in Edmonton.
Minus No. 1 goalie Tuukka Rask after the Vezina Trophy finalist left the bubble during Boston’s five-game victory in the opening round over the Carolina Hurricanes because of a family emergency, the Bruins never really got going in the restart after sitting first in the NHL when the schedule was halted by COVID-19 in mid-March, but put together their best effort of the summer in their final outing.
Boston, which lost to the St. Louis Blues in Game 7 of last year’s Stanley Cup final, dropped all three games in the round-robin seeding tournament to fall from the No. 1 slot down to No. 4.
And like their five-game defeat to the Lightning in the second round in 2018, the Bruins won Game 1 before losing four straight.
WATCH | CBC Sports’ Rob Pizzo recaps Sunday in the NHL playoffs:
Halak made a huge pad stop on Palat, who scored the winner in Tampa’s 4-3 OT victory in Game 2, one minute into the second overtime on a broken play as the Lightning came close before Maroon’s winner.
Boston came out flying to open the first overtime, forcing a couple of big stops from Vasilevskiy.
Krejci was assessed a tripping penalty to send the Lightning on the man advantage, but Halak made a couple of nice stops to keep his team alive.
The Lightning, who beat the Columbus Blue Jackets twice in overtime in the first round, including one that went five extra periods, went with 11 forwards and seven defencemen for the fourth straight game as blue-liner Ryan McDonagh returned after getting hurt in the opener. But they were down to 10 skaters up front when Nikita Kucherov left in the second period after taking a high stick from Zdeno Chara in the first.
After the teams traded goals in the second period, Cirelli gave Tampa the lead with 7:57 left in the third when he tipped Hedman’s point shot past Halak for his third.
The Bruins pushed facing elimination, and got a bounce with 2:33 remaining when Chara’s shot hit Palat’s stick and went right to Krejci, who buried his fourth into an open net with Vasilevskiy out of position for his team’s first goal at even strength since the third period of Game 2.
Boston actually had a chance to win it in regulation when Hedman went off for tripping with 1:56 left, but Tampa held on and forced the extra period.
Earlier in the third, Boston’s Karson Kuhlman raced around Tampa defenceman Luke Schenn, but Vasilevskiy, another Vezina finalist, outwaited the speedy winger to make the stop early in the third.
Boston then lost blue-liner Charlie McAvoy when Cedric Paquette drilled him from behind in the boards — a hit that went uncalled and had the Bruins bench steaming mad. McAvoy stayed down for a while before being helped to the locker room, but eventually returned to the action with his team desperate for that equalizer.
Tampa grabbed a 1-0 lead at 4:21 of the second when Palat bagged his fifth goal in the last four games after not scoring in the Lightning’s nine previous post-season contests. Shattenkirk took a shot from the point that Palat deftly redirected from the slot over Halak’s glove and off the crossbar.
Boston, which avoided elimination in last season’s first round at Scotiabank Arena in Game 6 against the Toronto Maple Leafs before winning that series and going on a long playoff run, got even when its power play clicked for a fifth straight outing. Krejci faked a shot at the point and slid a pass to Pastrnak, who wired his third past Vasilevskiy from the left circle at 12:38.
Kucherov, who took that high stick from Chara in the first, was in the box for tripping and went to the Tampa locker room for a second time shortly after Boston tied it and did not return.
The Lightning, who dispatched Columbus in five games in the opening round, came close to regaining the lead moments later, but Halak denied Palat of his second with a great post-to-post save before Zach Bogosian’s point shot hit the post.