"I wasn't waiting to see what he was doing, put it that way," said Fleury, who made 25 saves.
The No. 1 pick in the 2003 NHL Draft, Fleury is 350-205-59 with two ties since making his debut on Oct. 10, 2003.
Kris Letang and Chris Kunitz scored, and Malkin and Phil Kessel each had two assists for Pittsburgh (35-24-8).
Gregory Campbell had a goal and an assist, and Cam Atkinson scored for Columbus (28-32-8). Goaltender Sergei Bobrovsky, who missed 19 games with a groin injury, made 28 saves.
"I felt pretty good. I felt better as the game went on and I felt more comfortable," Bobrovsky said.
Columbus coach John Tortorella said, "There's some rust there, but for his first game he played very well. I'm encouraged how he played."
Campbell's first goal in 47 games, at 5:05 of the first period, capped a sequence that started at the other end with a shot by Pittsburgh defenseman Justin Schulz. The puck bounced off Bobrovsky's shoulder, fell behind him off his right skate, and landed inches from the goal line before it was cleared. The Blue Jackets transitioned with Rene Bourque passing ahead to Jared Boll, who found Campbell for a one-timer. Boll got his first assist since Feb. 7, 2015.
Letang tied it 1-1 at 14:23 on the power play with a shot from the high slot. His second goal in as many games was his 14th. The Penguins took a 2-1 lead 45 seconds into the second period when Kunitz scored from the left paint for his 13th goal.
"They're really good at intercepting passes. They're really good at taking away seams," Columbus captain Nick Foligno said. "Anytime you're trying to force something against a team like that, it's tough.
"You have to play against the boards and win the battles. They were doing that against us tonight. We didn't have the same focus, the same mentality. That was the difference."
The Penguins said they were ready for a heavy game from the Blue Jackets.
"We did a really good job of matching their intensity and aggression and we came out winning," Hagelin said.