Pittsburgh battled back from three goals down to tie the game heading into the third period, but Boone Jenner's second goal of the game restored Columbus' lead, 4-3, with 12:39 remaining. Derek MacKenzie added an empty-net goal.
"I like it that we stuck with it," Blue Jackets coach Todd Richards said. "We weren't perfect. There are areas where we have to be better, but the bottom line is we found a way to win. Boone does a really good job down low, dragging the puck.
After allowing two goals on 12 shots in Columbus on Sunday, Penguins goalie Marc-Andre Fleury seemed like he was on his way to another rough outing, allowing two goals on the first three shots he faced.
Dubinsky scored the Blue Jackets' first goal, 1:04 into the game, after the puck got through Brandon Sutter and Paul Martin in the corner. Dubinsky wristed a shot into the upper-right corner of the net past Fleury's glove.
Jenner's first goal, a deflection off a shot from Jack Johnson, gave the Blue Jackets a 2-0 lead 8:35 into the first.
"I have to give credit to my linemates and my teammates," Jenner said. "We all worked pretty hard tonight. It was kind of a different game, going up three and then [allowing] three. So when it was tied going into the third, we just wanted to stick to our game and I thought we did that."
The Penguins announced after the game that goalie Tomas Vokoun underwent a procedure to dissolve a blood clot Saturday and is out indefinitely, putting more emphasis on Fleury heading into the regular season and with Jeff Zatkoff now the backup goaltender.
Penguins general manager Ray Shero said Vokoun is resting comfortably. He also said he expects Fleury to face more pressure with Vokoun out.
"Tomas was undergoing the procedure during the game," Shero said. "[Fleury's play] has been OK. It's been a work in progress. If Tomas is out for a little while, it's going to be a situation where Marc's going to have to step up."
Fleury allowed a third goal, scored by Cam Atkinson 2:30 into the second period, but Jokinen erased the deficit with his natural hat trick.
Malkin found Jokinen charging toward the Columbus net to set up his first goal, a backhander past Sergei Bobrovsky, cutting the Blue Jackets' lead to 3-1. The two hooked up again, with Malkin backhanding a pass to Jokinen, who deked Bobrovsky and slid the puck past the goal line, bringing the Penguins to within 3-2 with 9:36 left in the period.
Jokinen is competing for the spot next to Malkin and Neal with second-year forward Beau Bennett. Penguins coach Dan Bylsma said Jokinen and Bennett have impressed when put in that situation.
"Beau played game one with James and Geno and played really well and showed a lot in that game," Bylsma said. "I think they had eight scoring chances as a group that game. Jussi is a guy who's played with some very good players in his career and has done very well.
"I'm not surprised to see him be able to fit in and play on that line and have some chemistry. He's an extremely intelligent player."
Jokinen completed his hat trick at 12:45, handling a pass from Neal and roofing a shot into the Columbus net.
"I think we were able to find chemistry right away," Jokinen said. "I think we were able to create some good chances in all three periods. I think some guys [you have chemistry with] right away. I just tried to fit in and I think those guys (Malkin and Neal) are pretty easy to play with.
"I think if you're playing with them or with Brandon Sutter or [Tanner] Glass, you have to be smart and change your game a little bit."
Pittsburgh held a 15-5 shot advantage after one period but failed to take advantage of several scoring chances, including an extended 5-on-3 with 5:27 remaining. The Penguins were able to distribute the puck through the Blue Jackets' crease to Neal multiple times, but the 40-goal-scorer couldn't solve Bobrovsky.
After allowing two power-play goals apiece Sunday, the penalty-killing units performed well. Columbus didn't allow Pittsburgh to score on five power plays, and the Penguins denied the Blue Jackets on two chances.