Oscar Lindberg's first career playoff goal made it 4-0, but then Game 2 four-goal hero Jean-Gabriel Pageau struck again, finally getting the Senators on the board.
Yet it was the Rangers who opened the scoring for the fourth straight game with Holden's perfectly placed shot between Anderson's blocker and pad at 14:04 of the first giving NY a 1-0 lead.
The New York Rangers have outscored Ottawa 8-2 in the last 120 minutes, both games New York held complete control of the game.
Turris scored 6:28 into overtime to lift the Senators to 5-4 victory over the New York Rangers on Saturday for a 3-2 series lead in their second-round series.
Nick Holden and Chris Kreider scored New York's other goals.
Turris now has three goals in these playoffs, and Ottawa can move on to the Eastern Conference Finals with a win in Game 6 on Tuesday night.
Any absence for the Senators' top defenseman would be detrimental to the remainder of the series, which is now tied after back-to-back Rangers win.
With Anderson out for the extra attacker, Brassard tied up with 1:26 to go when he was able to knock a rebound out of the air and it bounced through a crowd past Lundqvist.
"They played well at home for their two games and we played at home for our two games and we've got a series", Boucher said. With an overbearingly quick pace and physical edge, NY constantly hemmed Ottawa in its own zone, established offense near the zone and created turnovers in advantageous positions.
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The Ottawa Senators answered the bell Saturday afternoon, and they're only one win away from delivering a knockout punch to the New York Rangers. Anderson didn't look good at allowing Holden to beat him high on the glove side at 5:13. The pesky power forward struggled in the first round against the Montreal Canadiens but now has two goals in three games as the Rangers surge back. Senators coach Guy Boucher said he wasn't concerned by that before the game - the team's approach should remain the same, he said - and such thinking proved prescient as the night wore on. They are just kind of the gritty, grinding game I bring.
Game 3 brought the teams to NY and finally brought the Rangers a big 4-1 win over Ottawa. When Tanner Glass was penalized for interference early in the second, Neil raced over and began punching Glass.
The Senators struck for two goals 33 seconds apart a short while later.
In a further blow to the Senators, Erik Karlsson appeared to aggravate his heel injury. In Game 2 of this series, the Rangers blew a 5-3 lead with three and a half minutes left in the third period and lost the game.
Karlsson left at the end of the second period with a very pained look on his face and didn't return to the game.
That gave the Rangers a goal from each of their four lines.
A lot can change can change in two minutes. A Ben Harpur shot was blocked and the Rangers made no mistake.
Lindberg also scored the Rangers' final goal in their Game 3 win, with Glass picking up an assist.