Ottawa lost Craig Anderson to a sprained ankle early in the third period when Rangers forward Chris Kreider slid into him, but replacement Ben Bishop earned the victory when Kaspars Daugavins scored in the seventh round of the shootout.
Elsewhere, Boston continued its strong road form with a win at Tampa Bay, the New York Islanders won in overtime to end Montreal's six-game winning streak, Vancouver scored twice in the third period to overcome Dallas, and New Jersey notched a comeback win over Washington.
Ottawa's Daugavins appeared to mishit his winning shootout attempt that beat Rangers goalie Henrik Lundqvist between the legs. Kreider was then stopped by Bishop to end the game.
Patrice Bergeron and Brad Marchand also scored for Boston, which improved to 6-1-1 on the road.
Tampa Bay got goals from Steven Stamkos and Cory Conacher.
Alex Burrows and Kevin Bieksa also scored for the Canucks, who ended a three-game losing streak, including a 4-3 defeat to the Stars in Vancouver last week.
Jamie Benn, Michael Ryder and Brenden Morrow scored for Dallas.
Washington led 2-1 entering the third period on power-play goals by Mathieu Perrault and Mike Ribeiro.
The East-worst Capitals dropped to 0-7-1 against the conference's top six teams.
Toronto's James van Riemsdyk scored twice to lead the Maple Leafs past the Buffalo Sabres 3-1, spoiling the NHL head coaching debut of Ron Rolston.
Winnipeg's Blake Wheeler scored his second goal of the game with 4:54 remaining to lift the Jets over the Carolina Hurricanes 4-3.
Florida's Jonathan Huberdeau and Peter Mueller each had two goals to help the Panthers snap a five-game losing streak with a 5-2 victory over the Philadelphia Flyers.
Columbus' Vinny Prospal scored with 24.7 seconds left, capping a comeback that lifted the Blue Jackets to a 3-2 win over the Detroit Red Wings.