Jake Guentzel scored four goals in the Pittsburgh Penguins' 8-5 thrashing of the Philadelphia Flyers, ending the first-round series in six games.
Guentzel is only the second player in National Hockey League history to score four consecutive goals - a streak uninterrupted by either team - in a playoff game, according to the Elias Sports Bureau.
Couturier had been the Flyers' post-seasonsaviour, returning from a serious leg injury to score the Game 5 victor and then open Game 6 with his third goal of the series just 2:15 into the game.
This is the third time the Avalanche had trailed 3-1 in a series since the franchise relocated to Colorado. A few minutes later, Guentzel scored two goals 10 minute apart - the first one was tallied seconds after Kris Letang leveled Couturier - to put the Pens ahead, 7-4.
The Flyers got a golden opportunity to tie the game with a power play with 13:45 left as Brian Dumoulin took a delay of game penalty.
Couturier is clearly hobbled but continued his clutch play, giving the Flyers a 1-0 lead 2:15 into the game.
The Penguins swept the three playoff games at the Wells Fargo Center.
Guentzel scored the second of his four goals in the game off an assist from Phil Kessel .
He tied the game at 4 with 54 seconds left in the second period off a Flyers turnover. He has three goals and five points so far in the series. His goal was still being announced when Carl Hagelin made it 2-1 when he was left all alone in front of the net for the easy goal.
The Flyers tied it on Andrew MacDonald's one-time laser from the right point with 4:12 to go in the second.
With the second period reaching the final minute, another defensive-zone turnover by Radko Gudas cost the Flyers again.
But the Flyers got another break on a penalty that should have gone against them when Travis Konecny held Sheary on top of him by the jersey, then cross-checked Sheary in the back as he skated back to the bench.
The insurance would prove necessary as seconds later another Flyers turnover led to a Pens score - this one coming off the stick of Patrick Hornqvist. "Look at our team last year and look at our team this year", he said. The so-called home ice edge in Philly lost some shine with large pockets of empty seats for a must-win Game 6.
Guentzel is the third Penguin - along with Mario Lemieux and Kevin Stevens - and the 35th player overall to score four times in a playoff game.