Chris Kreider scored twice for the Blueshirts with Dan Boyle, Mats Zuccarello and Tanner Glass also netting.
Curtis Lazar scored the only goal for the Senators who hold the final wild card spot in the Eastern Conference.
The Western Conference Anaheim Ducks joined the Rangers on 101 points with a 3-2 overtime victory over the Boston Bruins.
Ryan Getzlaf scored the vital goal in the extra period for the Ducks while the losing point could prove vital for the Bruins in their play-off efforts.
The defending champion Los Angeles Kings moved into a play-off spot with a 3-2 win over the New York Islanders.
Anze Kopitar grabbed the game-winning goal with less than four minutes to go to seal the Kings’ third consecutive win.
The Winnipeg Jets hold the final wild card spot in the west and they boosted their chances of making the post-season with a 5-2 victory over the Montreal Canadiens.
The Florida Panthers moved to within three points of a wild card and condemned the Toronto Maple Leafs to a seventh straight defeat with a 4-1 win at the Air Canada Centre.
Sam Gagner scored the crucial overtime goal as the Arizona Coyotes beat the Buffalo Sabres 4-3 and the Washington Capitals also needed the extra period to beat the New Jersey Devils 3-2, Matt Niskanen with the winner.
In the day’s other games, the Carolina Hurricanes beat the Pittsburgh Penguins 5-2, the Detroit Red Wings went down 6-4 to the San Jose Sharks, the Nashville Predators were 3-2 winners over the Tampa Bay Lightning and the Colorado Avalanche downed the Vancouver Canucks 4-1.