The Senators (31-22-8) moved within two points of first-place Boston in the Northeast Division and one point behind Pittsburgh and Philadelphia for fifth place in the Eastern Conference playoff race.
Karlsson opened the scoring 1:08 into the first period with his 11th goal of the season on a sharp-angle shot from the corner to the left of Islander goaltender Kevin Poulin. Spezza, who has seven goals and eight assists in his past six games, made it 2-0 just 27 seconds later with his 26th goal of the season.
It was the third shutout of the season for Anderson (28-19-6). The 30-year-old moved into a tie with Henrik Lundqvist of the New York Rangers for fourth place in goalie wins this season.
HURRICANES 5, CAPITALS 0
In Raleigh, N.C., Eric Staal had two goals and an assist and Justin Peters cruised to his first NHL shutout as Carolina routed Washington.
Justin Faulk and Anthony Stewart scored in an 88-second span and Andreas Nodl added a goal during Carolina’s three-goal first period.
Peters needed to make just 17 saves to win his second consecutive start. He replaced Cam Ward, who was out with an undisclosed lower body injury.
Jiri Tlusty had two assists, giving him points in a team-best eight games in a row. Carolina led 4-0 after 40 minutes and won its third
in four games, improving to 11-3-1 in its past 15 at home.
Tomas Vokoun allowed two goals on seven shots before he was pulled after roughly five minutes.