The Senators (37-24-9) have won three games in a row, improving to 14-3-2 in 19 games since Jan. 25. They are two points behind the idle New York Islanders for the second wild card into the Stanley Cup Playoffs from the East.
Shane Pinto and Warren Foegele scored, and James Reimer made eight saves for Ottawa.
Conor Sheary scored and Igor Shesterkin made 31 saves, but the Rangers (28-34-9) lost their fifth in a row.
They tied a team record for fewest shots on goal in a game with nine. The record dates to Dec. 11, 1955, when New York had nine shots on goal in a 2-0 loss at the Detroit Red Wings.
Mika Zibanejad played in his 1,000th NHL game.
Pinto gave the Senators a 1-0 lead on a power-play goal with a wrist shot from inside the right face-off circle at 6:30 of the first period. Claude Giroux set it up with a pass off the right wall after he received a diagonal pass from Jordan Spence from the left point.
Ottawa extended its lead to 2-0 at 6:46 of the second period, when Lars Eller set up Foegele for a snap shot from the bottom of the right circle off a defensive zone turnover by Rangers defenseman Connor Mackey.
The Senators were 1-for-6 on the power play and outshot the Rangers 13-2 in the first and second periods.
Sheary scored on New York’s seventh shot of the game at 7:03 of the third period to cut it 2-1. He went to the net and redirected Tye Kartye’s pass off the rush from below the right circle.
Ottawa played the final 33:14 with four defensemen.
Thomas Chabot didn’t return after the first intermission. He was injured late in the first period when J.T. Miller appeared to hit him in the right arm. Lassi Thomson, who was playing in his first NHL game since Nov. 25, 2022, limped off the ice with a lower-body injury after Foegele scored.