Gustav Nyquist gave Columbus a 1-0 lead at 8:37 of the first period by diving to tap in a loose puck on a power play before Pittsburgh scored five straight.
Radim Zohorna and Guentzel scored 36 seconds apart in the second period.
Zohorna tied it 1-1 at 2:40 on a wrist shot from the slot off a rebound. Guentzel gave Pittsburgh a 2-1 lead at 3:16 by taking a pass from Crosby through the crease for a wrist shot from the right face-off circle for his 30th goal of the season.
"We're learning as a team we can give up a goal, and sometimes two, we can come back," Blue Jackets forward Sean Kuraly said. "It's just when you give up a few. It's a tough mountain to climb against world-class players and team. Not taking anything away from them, but we think we can be in games like this, no question.
"If we lose in a tight one, we lose in a tight one. But from our point of view, 20 guys, we can be better."
Rust made it 3-1 at 7:28. After tipping the puck away from Blue Jackets forward Cole Sillinger, Rust drove to the net past Sillinger and below defenseman Vladislav Gavrikov for a wrist shot.
Guentzel extended the lead to 4-1 at 14:06, when a snap shot from Crosby deflected off him.
"We have something special here," Guentzel said. "We just have to be ready to go down the stretch. We just have to make sure we come together as a team as fast as we can."
The Penguins outshot the Blue Jackets 32-14 in the first two periods, including 20-7 in the second.
"If we're not playing with structure, they're going to make us pay," Columbus defenseman Zach Werenski said. "Thought we started off the game well. They're getting some chances. I thought [Korpisalo] made some big saves. Then in the second there, they have their push and we don't really have an answer for it."
