Pavelski, the 36-year-old veteran, tied it with 6 minutes, 45 seconds left in regulation and then laid out to block a shot in the first overtime before Perry scored the winner in double OT, and the Dallas Stars avoided elimination Saturday night by beating the Tampa Bay Lightning 3-2 to force a Game 6 in the Stanley Cup Final.
It was one of two goals on the night for Perry, the 35-year-old veteran, and the victory prevented -- at least for a couple of nights -- Tampa Bay from securing its second Stanley Cup title in franchise history.
"Get one, keep going," Perry said. "We start building here and I think we're starting to do something special."
Anton Khudobin made 39 saves, and Perry prolonged the series by scoring 9:23 into the second overtime. It was a manner of redemption for the Stars a night after they lost in OT on a questionable penalty call when Tampa Bay scored on the ensuing power play. Game 6 is Monday night in Edmonton, Alberta. The Lightning lead the series 3-2.
"With how they play, I don't know if you can call them old," Stars center Tyler Seguin said of Pavelski and Perry. "They seem to have the best endurance of all of us. Joe keeps getting the late goals and Perry played a great game."
The Stars did it despite going down to five defensemen for half of regulation after Andrej Sekera took a Mikhail Sergachev shot off his right knee and missed all of the second period. Sekera returned for the third, a gutty performance that might have saved a team that looked to be running on fumes.
"That shows you his compete [level]," Stars coach Rick Bowness said of Sekera. "Give him a ton of credit for coming back. That was tough."
Dallas might have to dip even further into its already-depleted depth in Game 6 if Sekera's injury is severe enough to add him to the long list of unavailable players. Forward Roope Hintz was the most recent to join that group when he was injured crashing into the boards Friday night.
The Stars didn't have much time to regroup after that difficult loss with the first set of back-to-back games in the Final since 2009 and just the second since the mid-1950s. Instead of the fatigue wearing them down, they were able to respond in a big way against a healthier opponent.
"They're a good team," Lightning defenseman Victor Hedman said. "They fought back."
Pavelski again led the way. In the Final for the second time in his career after losing in 2016 with San Jose, he followed his two-goal performance in Game 4 with a season saver 24 hours later by scoring on a rare rebound allowed by Andrei Vasilevskiy.
The goal tied Pavelski with Tampa Bay's Brayden Point for the most goals this postseason with 13. It was the 61st of his playoff career, the most among American players.
Asked Friday night about tying that record, Pavelski deadpanned: "Keep it. Next question." Thanks to another strong performance from him and fellow veteran Perry, there will be plenty more questions going into Monday.
Some of those belong to Tampa Bay, which blew a 2-1 third-period lead and lost for just the third time in one-goal games this postseason. How to contain a suddenly dangerous Dallas top line led by Pavelski, along with Perry, is one of them.
Another is the health of defenseman Ryan McDonagh, who was slow to get up after a big hit in the first overtime. That was around the same time Pavelski blocked a point-blank shot by Point to keep the game going.
Perry finished it by putting a rebound home for his second goal of the game.
Tampa Bay again played without injured captain Steven Stamkos. He has played in just one postseason contest, Game 3 of this series, in which he scored in the first period.
The Associated Press contributed to this report.