Milan Michalek also scored for the Senators, who have won five straight at Madison Square Garden and seven of eight there (7-0-1).
New York (27-10-4), which entered with the most points in the NHL, had won five straight and 10 of 11.
Anderson's seventh career shutout came nearly two years after Ottawa's winning streak began in New York with a 2-0 victory on Jan. 14, 2010. Ottawa became one of the last teams to register a shutout this season. The Blackhawks and Islanders are the only remaining teams without one.
Henrik Lundqvist made 21 saves for the Rangers, who had their fourth winning streak of at least five games stopped.
BRUINS 2, CANADIENS 1
BOSTON (AP) — Jordan Caron and Milan Lucic scored, and Tim Thomas stopped 33 shots to lead Boston over Montreal.
Carey Price made 28 saves for Montreal, which lost to Boston for the third straight time and fell to 3-8 since Randy Cunneyworth took over as coach.
Yannick Weber scored for the Canadiens.
Montreal won the first two matchups against the defending Stanley Cup champions, winning home-and-home games at the end of October. But since then the Bruins have won 25 of 30 games.
After the game, the Canadiens said they traded forward Michael Cammalleri to the Calgary Flames for forward Rene Bourque. Cammalleri left the game after the second period.
CANUCKS 3, BLUES 2, OT
ST. LOUIS (AP) — Daniel Sedin scored a power-play goal 46 seconds into overtime to give Vancouver a victory over St. Louis in a matchup for first place in the Western Conference.
Alexandre Burrows had two goals and drew the decisive penalty for the Canucks, who have an NHL-best 59 points — three more than St. Louis. David Backes was whistled for boarding with 19.9 seconds to go in regulation, and the Blues were in disarray in overtime after defenceman Roman Polak broke his stick shortly before Sedin beat Brian Elliott from the right faceoff dot.
Jason Arnott scored both goals for the Blues, who lead the Central Division by a point despite the end of a four-game winning streak.
FLYERS 3, ISLANDERS 2
UNIONDALE, N.Y. (AP) — Sergei Bobrovsky stopped 33 shots, and Philadelphia beat the New York Islanders for the 26th time in 28 games.
Scott Hartnell, Wayne Simmonds and Sean Couturier scored for the Flyers (26-12-4), who moved within two points of the Atlantic Division-leading New York Rangers. Kyle Okposo and John Tavares scored for the Islanders.
The Flyers (26-12-4) have won 12 of 13 on Long Island during their dominant run against the Islanders. New York (15-20-6) had won three straight at home, including a 5-1 victory over Detroit on Tuesday.
Bobrovsky stopped Michael Grabner on a penalty shot 2:49 in and made a spectacular glove save on the Islanders right wing late in the second. The 23-year-old Russian has tormented the Islanders since joining the Flyers before last season, going 7-0 against New York.
RED WINGS 3, COYOTES 2, SO
DETROIT (AP) — Pavel Datsyuk and Henrik Zetterberg scored in the shootout, and Detroit beat Phoenix for its 13th straight home win.
Valtteri Filppula, Johan Franzen scored in regulation for the Red Wings, who moved within one home win of matching the team's best streak. Jimmy Howard stopped 25 shots to earn his 100th career NHL win.
Radim Vrbata, Taylor Pyatt scored regulation goals for Phoenix, and Vrbata added one in the shootout. Mike Smith made 40 saves.
HURRICANES 5, LIGHTNING 2
TAMPA, Fla. (AP) — Jiri Tlusty had two goals and an assist, Tuomo Ruutu added a goal and two assists, and Carolina defeated Tampa Bay.
Tlusty scored twice during Carolina's four-goal first, helping the Hurricanes take a 4-1 lead. Jay Harrison and Tim Brent also scored for the Hurricanes, who had lost four of five. Eric Staal had three assists, giving him 301 in his NHL career.
Tampa Bay got goals from Nate Thompson and Teddy Purcell, but the Lightning dropped their fifth straight (0-4-1).
PREDATORS 3, AVALANCHE 2, OT
NASHVILLE, Tenn. (AP) — David Legwand scored his second goal of the game at 4:26 of overtime, and Nashville rallied from a two-goal, first-period deficit to beat Colorado.
Legwand scored the winner on a rebound of his own shot.
The Predators have won seven straight over Colorado and nine of 10 overall in the series, dating to Feb. 4, 2010.
Legwand started the comeback with a goal in the second period, and Sergei Kostitsyn tied it in the third. Nashville has won three straight and six of seven.
Ryan O'Reilly had a goal and an assist, and Gabriel Landeskog added a goal for Colorado.
The Avalanche outshot Nashville 15-7 in the first period, but the Predators held a 35-29 edge for the game.