Kuznetsov’s overtime strike sealed a dramatic 2-1 win for the Caps as the 2016 and 2017 champion Penguins bowed out before their home fans at the PPG Paints Arena.
The win handed Washington a 4-2 series win and sees them advance to a showdown against the Tampa Bay Lightning for a place in the Stanley Cup finals.
After a scoreless first period, Washington took the lead through Alex Chiasson early in the second. Kris Letang levelled for Pittsburgh with a long-range effort which deflected off a stick and past Braden Holtby.
After a nerve-wracking third period which saw both sides fail to break the deadlock, the game went to overtime.
The decisive moment came at 5:27 when the Penguins gave up possession cheaply to leave the Caps with a breakaway.
Russian star Alex Ovechkin slipped the puck to Kuznetsov, who darted through the Penguins defense before beating goaltender Matt Murray with a clinical finish.
“We believe in each other,” Ovechkin said afterwards. “It doesn’t matter what happened in the past. We have to stick together.
“We knew it was there. We just had to battle, and we just had to fight through it. Again, great feeling right now and we’re going forward.”
Penguins coach Mike Sullivan said his team would learn from the loss.
“I think sometimes we all learn more from our failures than we do our successes,” Sullivan said. “I think this group knows how hard it is to win in the playoffs.
“All the teams are really good. There’s a fine line between winning and losing. We haven’t tasted this in a long time, and that’s a credit to the group of players in that dressing room.”
In the night’s other game, Nashville scored a series-levelling 4-0 win over the Winnipeg Jets to set up a decisive game seven in the Western Conference.
Predators goaltender Pekka Rinne made 34 saves while Viktor Arvidsson and Filip Forsberg scored two goals apiece.
Game 7 takes place in Nashville on Thursday.