Gaudreau had two assists, Kent Johnson and Eric Robinson scored, and Jon Gillies made 24 saves for the Blue Jackets (24-44-8), who had lost four straight (outscored 23-5 during stretch).
Marchenko has scored 21 goals in 53 games this season, passing Pierre-Luc Dubois (2017-18) for the most by a rookie in Blue Jackets history. He also tied Matty Beniers of the Seattle Kraken (73 games) and Wyatt Johnston of the Dallas Stars (76) for the most goals by a rookie this season.
"It's very cool," Marchenko said. "I'm very happy to score these 21 goals and the last goal here at the home rink. On the trip, it's not as much fun, but here, it's our fans.
"It's a first for me, the first goal in overtime. It's a great feeling. I really like it. I want to score more, of course, but it's a really good feeling. Great pass from Johnny, I just take [the] puck and shoot."
Boone Jenner tied it 3-3 at 14:11 of the third period, skating into the puck after Artem Zub poked it away from Marchenko in the left circle.
Johnson gave Columbus a 1-0 lead at 2:41 of the first period, scoring blocker side from the right circle on a power play.
Gambrell tied it 1-1 at 4:00 when he crashed the net and redirected in a centering pass by Erik Brannstrom.
Robinson scored five seconds later from the left circle to put Columbus back in front 2-1.
"They've got lots of skilled players who can score goals," Brannstrom said. "We've got to be ready from the start."
Kastelic tied it 2-2 at 9:26 on a rebound in the right circle. The goal happened after Gillies lost the blade of his right skate, got turned around and made a pad save on a point shot by Tyler Kleven.