Carl Hagelin had a goal and an assist, while Benoit Pouliot, Chris Kreider, Brad Richards and Brian Boyle also tallied for the Rangers.
New York were 5-0 up before Joffrey Lupul finally scored for the Leafs, who had been on a three-game winning streak before the match.
Clarke MacArthur scored less than a minute into overtime to give the Ottawa Senators a 4-3 win over the Montreal Canadiens.
Erik Condra, Colin Greening and Mark Stone scored to put Ottawa 3-1 up, but Montreal, who got two goals from Daniel Briere and one from Brian Gionta, rallied to send the game into OT.
Ryan Suter bagged a hat-trick as the Minnesota Wild beat the Washington Capitals 5-3.
Nino Niederreiter and Jason Zucker also scored for the Wild as they rallied from two goals down in the first period.
Patrick Berglund scored twice as the St Louis Blues stretched their winning run to five games by beating the Columbus Blue Jackets 6-2.
Torey Krug contributed two goals and an assist to lift the Boston Bruins to a 4-1 victory over the Winnipeg Jets.
Nathan MacKinnon's double helped the Colorado Avalanches edged out the San Jose Sharks 4-3, while the Philadelphia Flyers were 5-3 winners over the Phoenix Coyotes.
The Detroit Red Wings saw off the Dallas Stars 5-1, the Buffalo Sabres edged out the New Jersey Devils 2-1 and the Carolina Hurricanes were 3-2 victors over the New York Islanders.
There were also wins for the Florida Panthers and the Los Angeles Kings.