Jake Guentzel pulled the Penguins to 4-2 on a wrist shot five-hole from the right face-off circle 21 seconds into the third.
Zucker scored again by finishing a pass from Malkin with a wrist shot to make it 4-3 at 3:16 for his sixth goal in five games.
"We'll take those two points," Zucker said. "But obviously, we know it wasn't the most ideal game for us."
Danton Heinen tied it 4-4 at 3:59, tapping in a pass from Rickard Rakell at the top of the crease.
"They just kept coming at us," Blue Jackets forward Patrik Laine said. "We were kind of scared to play, make plays that were there. At the end of the day, just have to find a way to win these games."
Pittsburgh outshot Columbus 40-17 after the first period.
"Tons of time left, we know we have the firepower to score," DeSmith said. "The crowd backed us the whole way. It was really loud there, maybe the loudest of the season."
Bemstrom gave the Blue Jackets a 1-0 lead on a power play at 4:02 of the first period. Cole Sillinger passed to the left circle, where Bemstrom dropped to one knee for a one-timer to end a 27-game goal drought.