Malkin tied it 3-3 on a one-timer with DeSmith pulled for an extra attacker after Barzal gave New York a 3-2 lead at 13:35 of the third period when he collected the puck at center ice, skated past Pittsburgh defenseman Pierre-Olivier Joseph in the left face-off circle and beat DeSmith with a wrist shot bar down.
Sidney Crosby scored the only goal of the shootout in the second round. DeSmith made saves against Jordan Eberle, Barzal and Josh Bailey.
"It's a huge goal for us," Penguins coach Mike Sullivan said. "I think we needed a win for our confidence. I love how our guys dug in down the stretch. … [Letang] makes a good pass. He puts it right in Geno's wheelhouse, and obviously he can really shoot the puck."
Aston-Reese tied it 2-2 on his rebound at 7:02 of the second period. The forward, who had shoulder surgery in August and missed the first 11 games of the season, had five shots on goal in 14:12 of ice time.
"There was just hesitation [before the surgery]," Aston-Reese said. "I know going into battles, whether it was a battle or a fight or just kind of cross-checking around, there was a chance of my shoulder potentially slipping out. So to not have to worry about that anymore and have that hesitation out of my game is huge for me, especially the way I play."