Jean-Gabriel Pageau played the heroe= in extra time for the OTTAWA squad, who will now move to Madison Square Garden with a 2-0 lead.
Pageau completed his hat trick with two goals in the final five minutes of the third period to allow the Senators to force the extra time.
He managed a fourth goal at 2:54 of the second overtime, to sow hysteria in the crowd.
It was a hard blow for the Rangers who had 3-1, 4-2 and 5-3 advances during the game.
Goalkeeper Craig Anderson, who appeared staggering on some Rangers goals, caught up with him and made 43 saves.
His counterpart Henrik Lundqvist blocked 28 of the 34 shots he faced.
Marc Methot and Mark Stone have also donned the needle for the Senators, who lead a 2-0 series for only the second time in their history.
It is a first since 2007, at the final of Association East against the Sabers of Buffalo.
Brady Skjei scored two goals for the Rangers. Chris Kreider, Derek Stepan and Michael Grabner added nets for Alain Vigneault’s team.
A duel with changing dynamics
From the outset, the Senators were given three numerical advantages, but they were not able to take a shot on goal.
In the second five-game, the Rangers charged the Senators by opening the shorthanded score. Stone could not keep a puck in opponent territory and Grabner completed a two-on-one with Jesper Fast to give the 1-0 lead to his troop.
Pageau created the tie before the end of the first period, but Alain Vigneault’s men added to the second period. Kreider moved the ropes on a veiled shot and Stepan scored the Rangers’ second short-handed goal by defeating Anderson with a good wrist shot at 13:10.
Fifty seconds later, Methot allowed the Senators to narrow the gap to 3-2, but Skjei quickly returned a two-goal lead to his side thanks to his third net of the playoffs.
The two formations exchanged a goal in the first minutes of the third engagement and the Rangers seemed on the way to creating equality in the series. It was at this point that Pageau took matters into his own hands.
The 24-year-old striker shifted a shot from team-mate Zack Smith and at the end of the third period, he redirected a Kyle Turris throw to force an extra time.
He became the first Senators player to scored four goals in a playoff game.