Max Pacioretty scored his first two goals for the Hurricanes (25-8-7), who have lost three straight after winning 11 in a row. Brady Skjei had a goal and an assist, and Antti Raanta made 15 saves.
"We're a confident group, and with short-term memory we'll forget about this," Skjei said. "It wasn't our game. We didn't play the way we needed to play for the whole 60 minutes.
"We just didn't have quite our A game. It's obviously nice to get a point, but I think we wanted a better effort and a better result."
Marchenko gave Columbus a 1-0 lead at 7:26 of the second period, scoring a power-play goal on a wraparound at the left post.
"It gave me more confidence, but I got two more goals, just kept shooting," Marchenko said. "It will be very good for me for the next game."
Marchenko then made it 2-0 at 9:02 with another power-play goal, this time scoring on a one-timer at the right hash marks after Johnson held in the puck at the blue line.
"We can't take bad penalties," Carolina coach Rod Brind'Amour said. "That's the killer. Little uncharacteristic things cost us the game. We still could have won the game very easily."
Pacioretty, who was playing in his second game this season, cut it to 2-1 at 11:20 when his backhand attempt deflected in off Blue Jackets defenseman Vladislav Gavrikov.
Skjei tied it 2-2 at 17:18 on a power play after Columbus defenseman Andrew Peeke's clearing attempt caromed to him in the high slot.
Pacioretty gave the Hurricanes a 3-2 lead at 18:56 with a power-play goal, scoring on a one-timer from the bottom of the right circle off a pass from Andrei Svechnikov.