Alexandre Burmistrov had a goal and an assist for Winnipeg (5-8-1), while Evander Kane recorded his fourth goal of the season and first in nine games.
Ondrej Pavelec made 23 saves as the Jets lost their third straight and fourth in a row at home, the longest home-losing streak for the team since the franchise moved from Atlanta prior to last season.
Just nine seconds into the third period, Marchand was breaking in alone on Pavelec when he was tripped up by defenceman Ron Hainsey.
The power play clicked 27 seconds later when Bergeron sent a pass to Marchand and he put a close backhand shot past Pavelec for the go-ahead goal.
Boston edged Winnipeg 9-5 in shots on goal in the scoreless first period.
The best opportunity for the Jets in the opening period was centre James Wright’s shot from the side of net that just didn’t have enough angle and banged off the post.
The teams made up for the lack of first-period scoring during the second with two goals each, including a pair in the last 27 seconds that made it 2-2.
With the Jets crowding the Boston net, the rebound from Zach Bogosian’s point shot was flipped into the net by Burmistrov at 1:43 of the second period.
The Bruins evened the score 1-1 with some help from Hainsey.
Seguin was credited with a deflected goal after Boston captain Zdeno Chara’s shot from the point eventually bounced into the net off Hainsey’s leg at 10:57.
Kane gave the Jets the 2-1 lead at 19:33 of the period when Nik Antropov sent a backhand shot from the backboards to the front of the net and Kane snapped in his own rebound.
But with just two seconds left on the clock, Paille deflected a long shot from Johnny Boychuk past Pavelec that tied the game at two heading into the final period.
Winnipeg pressed for the tying goal in the dying seconds, but Rask kept the puck out as Boston won the second game of a five-game road trip.
Notes: The Bruins were without winger Milan Lucic, who arrived in Winnipeg Saturday but left the same day to return to Boston for what the team called personal reasons … Veteran winger Jay Pandolfo, 38, was playing his first game with the Bruins after signing a one-year contract as a free agent on Feb. 12. … Jets defenceman Mark Stuart was playing in his 400th NHL game. His first 283 were with Boston.