The team lost standout goalie Craig Anderson to a sprained right ankle at 1:43 of the third period after Rangers forward Chris Kreider was tripped in front and slid into the unsuspecting netminder.
No penalty was called on the play and Anderson, who is listed as day-to-day, had to be helped to the locker-room.
The Senators, already decimated by injuries to defenceman Erik Karlsson (Achilles) and centre Jason Spezza (back), can ill-afford to lose their No. 1 goalie for an extended period of time.
"My heart sank into my stomach when it happened," said defenceman Marc Methot, who got tangled up with Kreider on the play in question. "It's the last thing we need. He's basically been the heart and soul of our team, or at least a large part of it. It's unfortunate, but it's the luck we're getting right now as a team."
The 31-year-old Anderson leads the league with a 1.57 goals-against average and a .950 save percentage, but Senators coach Paul MacLean says the only thing the team can do is look at the injury as yet another opportunity for someone else in the organization.
That appears to be goaltender Robin Lehner, who will be recalled from Binghamton of the American Hockey League and is expected to arrive in Ottawa on Friday.
"It's creating great opportunities for young players," said MacLean. "We've always talked about what great depth we have in this organization and how many good young players that we have playing in Binghamton and we're finding out that we do have a lot of great young players because now they're all playing here in Ottawa and they're finding a way to win a game."
Anderson didn't speak to the media after the game, but posted to his Twitter account that: "My ankle's gonna be ok, be back (as soon as possible)."
Lost in the wake of Anderson's injury, was the fact the Senators didn't crumble and managed to win their third straight game.
Kaspars Daugavins scored in the seventh round of the shootout and backup goalie Ben Bishop picked up the victory in relief of the injured Anderson.
Daugavins appeared to fan on his winning shootout attempt that fooled Rangers goalie Henrik Lundqvist between the legs. Kreider then stepped up needing to score, but couldn't beat Bishop.
"I was actually a little lucky," said Daugavins with a big smile.
Jakob Silfverberg also scored in the shootout for Ottawa, while Ryan Callahan had the lone goal for the Rangers.
Silfverberg and Mika Zibanejad scored for the Senators (10-6-2) in regulation. Anderson stopped all 21 shots he faced before being replaced by Bishop, who allowed two goals on 13 shots.
Callahan and Ryan McDonagh scored goals 51 seconds apart in the third period for the Rangers (8-7-1). Lundqvist made 35 saves in taking the loss.
Bishop said he felt a little sick seeing Anderson go down, but added there was little time to dwell on it.
"You want to know if he's OK at first, but once the puck drops you've got to do your job," said Bishop. "It's one of those things that as cold as you can be once the puck drops, you're in the game."
Trailing 1-0 but with Anderson out of the game, the Rangers tied it at 10:44 of the third period on a power-play goal by Callahan and then quickly took the lead on McDonagh's shot from the point to silence the already stunned crowd of 19,076 at Scotiabank Place.
But with the tables turned, Zibanejad tied the game with a power-play goal from in close with just over six minutes remaining to send the game to overtime.
"We got that first one and then we were able to get the lead and at least we got a point," said Rangers defenceman Marc Staal. "We found a way to get back in the game."
Thursday was the first meeting between the two teams since the Rangers eliminated the Senators in Game 7 of last year's Eastern Conference quarter-finals.
The Senators opened the scoring at 6:48 of the first period on a highlight-reel short-handed goal by Silfverberg. The Swedish rookie beat New York defenceman Michael Del Zotto in a race for the puck in the Rangers end, looked up as if he was going to pass, but instead beat Lundqvist with a backhand into the top corner.
"It gives me a lot of confidence," said Silfverberg. "(Lundqvist) is one of the best goalies in the league and he's one of the best goalies Sweden ever had."
Del Zotto then had a great chance to tie it up on the power play, only to be robbed by a sprawling Daniel Alfredsson in the Ottawa crease.
The game slowed down in the second with neither team generating many chances. Silfverberg had a decent opportunity early in the period, but Lundqvist made a good save.
Notes: Apart from Karlsson and Spezza, Ottawa was without LW Milan Michalek (knee, day-to-day), C Peter Regin (day-to-day), D Jared Cowen (hip, out for season), RW Guillaume Latendresse (whiplash, day-to-day). D Mike Lundin and C Jim O’Brien were a healthy scratches. The Rangers were missing RW Rick Nash (undisclosed, day-to-day), C Darrol Powe (concussion, indefinitely), D Michael Sauer (concussion, indefinitely). D Steve Eminger and RW Arron Asham were healthy scratches.