Kris Letang gave Pittsburgh a 1-0 lead at 2:03 of the first period when his soft wrist shot from the right point hit Islanders defenseman Ryan Pulock and deflected past Varlamov.
It was the second straight game Varlamov allowed an early goal; Penguins forward Bryan Rust scored 3:22 into Game 2.
"I'll have to look at [the game] again," Islanders coach Barry Trotz said when asked about Varlamov. "We'll have to look at it. Sometimes your first reaction might not be favorable, but I'm going to look at all the chances and the goals and see what we could have done."
Mayfield tied it 1-1 at 11:03 of the second period when he took a pass from Barzal, deked Penguins forward Zach Aston-Reese and roofed a wrist shot over Jarry's glove.
"I think no matter what, when you lose, it's tough," Mayfield said. "That's really all I care about, so it's tough going down 2-1, losing one at home. But that's the beauty of playoffs, you can bounce right back in two days. We've just got to refocus and have a good start on Saturday."
Carter restored Pittsburgh's lead 2:31 later with a wrist shot off the left post from the right circle to make it 2-1 at 13:34. Jason Zucker pushed the lead to 3-1 at 18:03.
NOTES:Malkin had two shots, one hit and two blocks in 12:10 of ice time. … Letang had two assists for his fifth three-point game in the playoffs, passing Larry Murphy for the most by a defenseman in Penguins history. … Pittsburgh's top line of Crosby, Rust and Jake Guentzel was held without a point. … Barzal and Islanders forward Jordan Eberle each scored his first point of the series with an assist on Mayfield's goal.