Gene J. Puskar, AP
Pittsburgh Penguins' Sidney Crosby (87) and Evgeni Malkin (71) pose with the the Prince of Wales Trophy after beating the Ottawa Senators 3-2 in the second overtime period during Game 7 of the Eastern Conference final in the NHL Stanley Cup hockey playoffs in Pittsburgh, Thursday, May 25, 2017. (AP Photo/Gene J. Puskar)

PITTSBURGH — It was said that the Penguins could not and would not reach the Stanley Cup Final without Kris Letang, that the slew of injuries they incurred during the second half of the regular season would crush them.

Or that, on the whole, they’d be entirely too tired, constantly hearing that teams coming off a long run the year before don’t have enough left in the tank to do it again, let alone in a year that also featured international competition.

But these Penguins, so resilient all season, shot holes in all of those arguments during a 3-2 double-overtime win over the Ottawa Senators in Game 7 of the Eastern Conference final on Thursday at PPG Paints Arena.

In the process, they shot themselves into the Stanley Cup final opposite Nashville, the series starting at home next Monday.

The shot that did it belonged to Chris Kunitz, whose blast at 5:09 of the second overtime won it. It was the second goal of the game for Kunitz, who hadn’t scored since Feb. 16.

The Penguins dictated the terms starting with the first overtime period, when they accounted for eight of the 10 shots on goal.

Phil Kessel had a gorgeous chance early in the first extra session but missed the net on a mini-breakaway. The frenetic pace kept up, and Kunitz nearly ended it when he batted a puck out of the air later in the extra session.

This couldn’t have been easy for Penguins goaltender Matt Murray as all this was happening, either. He didn’t see a shot in overtime until one from Kyle Turris at 11:26 appeared to catch him in a sensitive area.

Kessel enjoyed an even better opportunity late in the overtime, his shot somehow going up and over goalie Craig Anderson. The puck appeared to sneak under the crossbar, but it actually floated atop the net, fooling some of the fans inside the building.

There was also a two-on-one with Carter Rowney and Bryan Rust, with Rust unable to get enough of a shot off.

No NHL team had reached back-to-back finals since Pittsburgh and Detroit in 2008 and 2009, but the Penguins made it for the sixth time in their history.

The Senators were bidding to make it for the first time since 2007 but instead dropped to 0-6 all-time in Game 7s. The Penguins improved to 10-7 in Game 7s. They’ve won seven of their past 10 and raised their record in them to 4-7 at home.

Since Penguins coach Mike Sullivan took over, the Penguins have rarely fallen into any sort of sustained funk, especially in the playoffs.

Sullivan talks often about resilience, about resetting a mindset, and he’s created a culture of ingesting results from one game, correcting the mistakes, then moving on to the next.

The funny part about Tuesday, though, was that the Penguins weren’t all that upset with their performance in Game 6. They simply ran into a hot goaltender in Anderson, who stopped 45 of 46 shots thrown at him. The 75 the Penguins attempted were a playoff-high for them.

The challenge, then, would be sticking with it, on repeating the same sort of effort.

That didn’t happen as perfectly as the Penguins would have liked — Game 7 started with Ottawa in the driver’s seat — but a bounce-back occurred in this one, too. They also had to keep attacking Anderson, who was stellar again.

Conor Sheary and Kunitz perfectly executed a two-on-one for a 1-0 Penguins lead at 9:55 of the second period, Sheary waiting just long enough before dishing to Kunitz for his first goal since Feb. 16.

The lead didn’t last long, however, as the Senators scored 20 seconds later, Mark Stone beating Murray on a high shot from the right circle.

It initially looked like the play might have been offside and worthy of a Penguins challenge, but replay showed Stone deftly dragging his left skate as Erik Karlsson entered the zone.

A game-time decision for this one, Justin Schultz pushed the Penguins in front, 2-1, at 11:44 of the third period with a power-play goal.

Phil Kessel drew a penalty, and Schultz beat Anderson with a breaking ball from the point. Kunitz provided a key screen.

That lead was also short-lived. Less than three minutes later, at 14:41, Ryan Dzingel banged in a fortuitous rebound — one that hit off Murray’s back — to force a 2-2 tie.

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