Fredrik Sjostrom scored for the Rangers in regulation as the Eastern Conference leaders stretched their winning streak to three.
Daniel Alfredsson had the lone goal for the Senators, who lost their fifth straight. They've scored only five goals during that span.
The Senators had a 9-8 shot advantage in an evenly played, scoreless first period.
Thanks to a pair of power plays, the Senators dominated the first half of the second period, but could not break through against Lundqvist. Alfredsson had the best chance on the first power play, unloading a hard shot from the left dot. Dany Heatley had a solid chance at the side of the net on the second.
Ottawa had eight of the first nine shots in the period. The persistence paid off with 3:47 remaining when Alfredsson got his first goal in 11 games. The Senators captain picked up the puck in the left corner and wheeled into the slot to beat Lundqvist with a wrist shot.
In the third, Lundqvist made a blocker stop on Vermette's short-handed breakaway in the opening minutes to prevent Ottawa from expanding its lead.
The save was a turning point, and the Rangers evened the score on Sjostrom's tally at 7:17. Marc Stall unloaded a hard shot from the point and Sjostrom knocked in the rebound for his second goal.
That set the stage for overtime.
New York's Michal Rozsival had the only shot in overtime, a sharp-angle bid in the final seconds. The Senators outshot the Rangers 28-27 heading into the shootout.
Notes: Wade Redden faced his former club for the first time since leaving the Senators to sign with the Rangers in July. The defenseman played the first 11 years of his career with Ottawa. … The Rangers and Senators meet again Saturday afternoon in Ottawa. Both teams play a home game in the interim: the Senators host Montreal on Thursday, and the Rangers face Vancouver on Wednesday. ... Ruutu returned for the Senators, having completed a two-game NHL suspension for elbowing Montreal's Maxim Lapierre in the head. ... Scott Gomez missed his third straight game for the Rangers with a bruised ankle. ... Rozsival played in his 500th game. ... Auld started for the 11th time in the last 12 games; Lundqvist made it 13 of 14.
