Daniel Alfredsson also scored for the Senators, who were outshot 39-20.
Milan Lucic scored on the power play about midway through the first period to give the Bruins a 1-0 lead. He converted a pass to the net by linemate Nathan Horton as Boston had a 20-5 advantage on shots in the opening period.
Alfredsson tied the score at 5:09 of the third and Rundblad got the winner while Boston's Rich Peverley was in the penalty box serving 4 minutes for a high sticking double minor.
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