Ryan Spooner and Eriksson went down the ice together and Spooner sent a pass across to Eriksson, who moved the puck with his skate onto his stick to set up his first goal of the pre-season 1:46 in OT.
Niklas Svedberg stopped 26 shots for the Bruins, who improved their exhibition record to 5-1-0. Pavelec faced 33 shots for the Jets (1-3-3).
The teams play a rematch Friday in Boston.
The teams were tied 1-1 heading into the third period after a scoreless second at MTS Centre.
Bergeron had the game's first goal when he took a feed from Brad Marchand and put a close, low shot past Pavelec at 3:54 of the first period for his first goal of the pre-season.
The veteran centre spent the off-season recovering from not one, but four injuries after Boston lost last year's Stanley Cup final in six games to Chicago.
During the final, Bergeron played some games with a broken rib, torn rib cartilage and a separated shoulder. He later found out he also had a collapsed lung.
Winnipeg had a good chance to tie the game shortly after Bergeron's goal when highly touted defensive prospect Jacob Trouba blasted a shot from just inside the blue-line.
However, Bruins centre Gregory Campbell splayed on the ice to block the shot. Campbell broke his right leg in Game 3 of Boston's sweep of Pittsburgh in last year's Eastern Conference finals.
Winnipeg did make it 1-1 with just under three minutes left in the opening period on a power-play goal by Setoguchi.
Bruin Matt Bartkowski blocked a shot and sent the puck back to Setoguchi, who beat Svedberg.
The scoreless second period was a good one for Svedberg, who made a number of sharp saves, especially during a Jets' late power play.
Winnipeg went up 2-1 on Scheifele's power-play goal at 4:21 of the third period.
Eric Tangradi dumped in a long shot that bounced off the end boards on the glove side of Svedberg. Scheifele picked up the puck, cut in front of Svedberg and flipped a backhand shot past the netminder for his first goal of the pre-season.
Boston only let the lead stand for two minutes after Matt Fraser stood in front of Pavelec and Spooner's shot went into the net at 6:22.
The Bruins had outshot the Jets 30-27 after regulation.
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