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.
Celebrity Breakups and divorces of 2014 [PHOTOS]