Rask held off the Islanders in the middle frame as Brad Marchand and David Krejci each tallied to put the Bruins on track for their fourth straight win.
Adam McQuaid also scored and Gregory Campbell added an empty-netter for Boston, which won for the seven in nine games overall.
Casey Cizikas scored and and Evgeni Nabokov was touched for three goals on 33 shots for New York.
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