The Flyers' second-round opponent will be the New Jersey Devils.
The Rangers and Senators were both 1-2 at home in the first six games of this series. Yet the Rangers had to be boosted by the boisterous crowd, which began cheering during the national anthem and never stopped.
This was the Rangers' first Game 7 win at home since June 14, 1994, when they beat Vancouver to win the Stanley Cup.
Unlike the offensive barrage that the Flyers and Penguins delivered, this was a tight defensive series. The most goals any team scored came in Game 1, when the Rangers earned a 4-2 win.
This didn't resemble the Rangers team that averaged 3.5 goals in going 6-0-0 against the Flyers in the regular season.
But with goalie Henrik Lundqvist on his game, the Rangers did enough to advance. Lundqvist was named the No. 1 star after stopping 26 shots.
Staal opened the scoring by converting a pass from Derek Stepan in the left circle with 15 minutes, 14 seconds left in the second period.
The Rangers made it 2-0 when Girardi converted a pass from Brandon Dubinsky in front of the net with 10:56 remaining in the second period. It was also Girardi's first goal of the series.
Daniel Alfredsson's slap shot on the power play cut the deficit to 2-1 with 8:26 left in the second period. It was the second goal of the series for the 39-year-old Ottawa captain, who missed three games with a concussion after being elbowed by the Rangers' Carl Hagelin in Game 2.
The Rangers were the aggressors early in the third period, though Ottawa put on the heat toward the end.
Neither team played conservatively in the first period, with end-to-end action both ways.
Contact Marc Narducci at 856-779-3225, email@example.com or on Twitter @sjnard.