Crosby scored two of Pittsburgh's three unanswered goals in the second period after Gaudreau gave Columbus a 1-0 lead in the first.
Rust tied it 1-1 at 1:15 of the second, falling to the ice for a wrist shot after Brian Dumoulin sent a shot off the end boards that bounced back under Merzlikins. Rust has two goals and four assists in his past two games after having two points (one goal, one assist) in his previous 14.
"Sometimes you get a little bit of luck, sometimes you don't," Rust said. "Sometimes you bury your chances, sometimes you don't."
Crosby put the Penguins ahead 2-1 at 2:02 on a rebound off a shot from Guentzel, diving to his left for a wrist shot from the slot.
Crosby made it 3-1 on a power play at 10:14 when a pass from Guentzel went in off him in the crease after deflecting off the stick of Blue Jackets defenseman Vladislav Gavrikov. The goal was upheld after Columbus challenged for goaltender interference.
"I couldn't go farther because he came on me. That one is a tough play," Merzlikins said. "They put the players on the backdoor right there, that corner. It's hard to push. But I saw on video, I think it hit [Gavrikov's] stick, if I'm not wrong. So, again, it's a tough one.
"I can't cheat. If I cheat, I'm going to get punished on the shot, especially in this league. ... I want that save; I want that save. I have to find the solution on that one."