Kelly's tally 5:56 into the final frame put the Bruins ahead 3-1 and Boston's Tim Thomas held off a furious Kings assault down the stretch to secure the victory.
The Senators beat Pittsburgh 8-4 Saturday.
At 89 points, the Bruins are holding down the East's second seed.
Slava Voynov and Colin Fraser scored for Los Angeles, but it wasn't enough to prevent the end of the Kings' six-game winning streak.
Jonathan Quick made 22 saves for Los Angeles.
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