Little beat Chad Johnson with a low shot between his pads, the only scorer in three rounds.
Winnipeg's Evander Kane tied the game at 1 with a wrister that beat Johnson over his glove with 1:57 left in the third period. Just a few minutes earlier, Kane had hit the post after fans started chanting ''Go Jets Go!'' to try to propel their team to a victory.
Brad Marchand scored the opening goal at 10:12 of the first period for the NHL-leading Bruins, who have clinched the top spot in the Eastern Conference and have 115 points to lead the NHL, three ahead of the idle Anaheim Ducks.
Winnipeg forward Olli Jokinen was called for holding with 40 seconds left in overtime, but Jets rookie goalie Michael Hutchinson made a snapping glove save on a blast from David Krejci with 7 seconds left to send it to a shootout.
Hutchinson stopped 32 shots in regulation and overtime, while Johnson made 36 saves. Hutchinson was drafted by the Bruins in the third round (77th overall) in the 2008 entry draft, and was signed by the Jets before this season.
The fans gave the Jets a standing ovation after the game, and the players skated to center ice and raised their sticks toward the sold-out crowd of 15,004 at MTS Centre. It was the third straight season the local fans bid farewell to the Jets without watching a playoff game, and the seventh season in a row the former Atlanta franchise has missed the postseason.
Marchand opened the scoring when he used Reilly Smith's dumped-in shot off the back boards to beat Hutchinson with a backhand shot.
Jarome Iginla almost added to the lead with a breakaway, but Hutchinson came out and stopped the wrist shot with just under four minutes to go in the period in which the Jets outshot the Bruins 12-6.
A scoreless second period saw Winnipeg defenseman Mark Stuart throw his weight around the ice. First, Stuart smacked into Loui Eriksson standing at the side of the Jets net and knocked him into the backboards. Eriksson wasn't injured and Stuart didn't draw a penalty. A few minutes later, Stuart sent Marchand to the ice with a high stick. Marchand got up slowly, but returned to action while Stuart was sent to the box.
Winnipeg leading scorer Blake Wheeler set up Kane's tying goal when he raced down the side of the ice and sent the pass to Kane in front of the net. It was Wheeler's 41st assist of the season and 64th point, which bumped up the career high he's set this season.
NOTES: The Jets had a 35-31 edge in shots on goal after regulation. ... Boston rested center Patrice Bergeron and defenseman Zdeno Chara. ... Winnipeg was without captain Andrew Ladd (elbow) and defenseman Dustin Byfuglien (upper-body), who won't play the final game.