The Senators stayed a point behind Boston for the lead in the Northeast Division.
Anderson gave up a goal to Brad Winchester 3:10 into the game, but it was all Ottawa from that point, with the Senators scoring four times on just 21 shots.
Greening then scored his 10th goal late in the second period and his 11th midway through the third.
Antti Niemi surrendered all four goals.
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