Ottawa, which had won its previous two games, got its lone goal from Antoine Vermette. His score came after the Senators had fallen behind 3-0.
Boston needed only 28 seconds to produce its first goal, which came when Kessel grabbed the puck off a draw and fired a shot from the right circle.
The Bruins built a 3-0 lead after one period and beat the Senators for the second time in nine meetings.
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