Danton Heinen scored twice, and Tristan Jarry made 29 saves for the Penguins (4-0-1), who scored at least six goals for the fourth time this season.
"In the first, we just got outworked and didn't execute well all the way through," Crosby said. "[Jarry] made some big saves. It could have been a bigger deficit than it was. He gave us a chance to get back into it in the second."
Kent Johnson scored his first NHL goal, and Elvis Merzlikins made 33 saves for the Blue Jackets (2-4-0), who led 2-0 in the first period and 3-1 in the second.
"It's tough to get wins in this league, and you're going to have to be up for a full 60 [minutes]," Blue Jackets captain Boone Jenner said. "Our start was good. We didn't have the same energy in the second and the third, so they're going to make you pay."
Jan Rutta brought Pittsburgh to within 3-2 at 10:04 of the second period on a one-timer, and Heinen tied it 3-3 at 14:19 from the right post after the puck popped out to him during a scramble.
"He's a guy who knows how to find the back of the net," Crosby said of Heinen. "He has a great shot, but he goes to the tough areas, too. We got a couple of goals doing that. As a group, we did that way better in the second and third periods."