Karlsson put home a rebound while on the power play at 5:27 of the first period to give Ottawa a 1-0 lead. On the ensuing faceoff, Kovalev collected a pass from Peter Regin and beat the Coyotes' Jason LaBarbera with a wrist shot at 5:36 -- the fastest two goals in Senators' history.
Ottawa goalie Brian Elliott picked up the victory by turning aside 28-of-30 shots.
LaBarbera was pulled after allowing three goals on 20 shots. Ilya Bryzgalov entered and yielded two goals on 16 shots the rest of the way.
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