Laine scored in the fourth round of the shootout when he tucked a puck under Bruins goalie Anton Khudobin. Danton Heinen's attempt on the other end to keep the game alive clanged off the post.
Tanev and Joe Morrow provided the goal scoring in regulation, and Connor Hellebuyck made 28 saves for Winnipeg, which won its fourth straight game in overtime and its sixth in a row overall.
David Pastrnak, Torey Krug, Heinen and Ryan Donato all scored for the Bruins. Khudobin finished with 28 saves as Boston capped its four-game road trip at 2-0-2 and fell to 4-2-3 in March.
Winnipeg kept within five points of Central Division-leading Nashville after the Predators' shootout win over the Minnesota Wild on Tuesday. Meanwhile, Boston pulled within one point of the Atlantic Division-leading Tampa Bay Lightning.
Tanev put a rebound past Khudobin to open the scoring with 14:27 left in the first period. Donato beat Hellebuyck with a backhander after a turnover to knot the score with 53 seconds left in the period.
Tanev restored Winnipeg's lead on a wrist shot 16 seconds into the second period before Morrow made it a two-goal game when he scored with 13:35 remaining in the middle frame.
Heinen gave the Bruins life with a power-play goal 1:45 into the third.
After Pastrnak's power-play strike at 3:36 of the third completed Boston's comeback to tie it at 3, Tanev put Winnipeg back on top with a short-handed goal with 15:31 remaining.
Krug added another power-play goal on a slap shot from the left circle to again knot the score with 11:54 to go. Both teams went scoreless in the back half of the third period and overtime, forcing the shootout.
Boston's Matt Grzelcyk left the game at the end of the second period after being hit from behind.
Boston returns home to face the Lightning on Thursday night. Winnipeg begins a four-game road trip Thursday against the Chicago Blackhawks.
--Field Level Media
Boston | Winnipeg | |
Torey Krug 2 | Points | Brandon Tanev 3 |
Torey Krug 1 | Goals | Brandon Tanev 3 |
Brad Marchand 2 | Assists | Adam Lowry 2 |
Torey Krug 1 | Power Play Goals | N/A |
N/A | Short Handed Goals | Brandon Tanev 1 |
Anton Khudobin .875 | Save Percentage | Connor Hellebuyck .875 |
Anton Khudobin 28 | Saves | Connor Hellebuyck 28 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Boston | 32 | 4 | 3-5 | 1-1 | 2 | 30 |
Winnipeg | 32 | 5 | 0-1 | 2-5 | 11 | 31 |