The Bruins spotted the Jets a 2-0 lead in the first period, but began a comeback with less than 4 minutes to go in the frame when Zdeno Chara scored on a power play.
Then Kelly went to work, scoring the equalizer on a short-handed tally 7:26 into the second period. He gave the Bruins the lead 9 minutes later when he one-timed a cross-ice pass from Benoit Pouliot past Jets goalie Ondrej Pavelec.
Brad Marchand added an empty-netter and Tim Thomas turned aside 40-of-42 shots, including all 16 he saw in the third period.
The Bruins have won 11 of their last 12 games.
Evander Kane and Dustin Byfuglien scored for Winnipeg and Pavelec finished with 32 saves.