Ben Bishop made 25 saves as the Ottawa Senators 1, at Scotiabank Place.
Zack Smith, Nick Foligno, Kyle Turris and Jason Spezza netted goals for the Senators, who earned their second straight win.
"I thought our team played real good from start to finish," Senators head coach Paul MacLean said. "I thought the physicality of the game was there on both sides and we were able to match it."
The Senators took a 2-1 advantage with 1:10 remaining in the opening period when Jim O'Brien grabbed an errant clearing attempt by the Rangers at the New York blue line and sent a wrister on net that was saved, but Foligno was there to clean up the rebound.
After a scoreless second period where Bishop made nine saves and Biron faced just three shots, Turris gave Ottawa a two-goal advantage at the 5:53 mark of the third when he cleaned up a rebound of a Daniel Alfredsson shot from the point.
Spezza's empty-net goal secured the outcome as Bishop made nine saves in the final stanza to finish off the top team in the Eastern Conference.
"It just wasn't a complete effort on both ends of the ice," said Callahan. "They buried their chances and we didn't buy ours."
Callahan opened the scoring 4:36 into the first period when he made a diving tip-in of a cross-ice pass from Brad Richards that beat Bishop to the glove side.
But Smith tied the game at one 74 seconds later with a slap shot from the top of the left circle after a Rangers' turnover at their own blue line.
Bishop improved to 2-0-0 for Ottawa since coming over in a trade from the St. Louis Blues...Ottawa improved to 18-13-3 at home this season, while New York fell to 20-10-5 on the road...The Senators took the season series by a mark of 3-1 to earn their first series win against the Rangers since 2007-08.