David Backes scored the winner 22 seconds into the extra period after the Blues rallied from a two-goal deficit.
"We had the good and bad right throughout the game," St. Louis coach Ken Hitchcock said. "Every part of our game was bad and good. Everybody had a piece in every part of the game -- their team, our team.
"We had good early then bad for a long stretch, then we started to come on again."
Backes scored his 16th goal off a turnover created by Alexander Steen at the blue line. The puck fell between Columbus' Fedor Tyutin and Artem Anisimov. Backes skated in, pulled the puck back and beat Mike McKenna for the Blues' third straight win.
"I find the loose puck, take it to the net and found a little bit of area there and was lucky to get it through," the St. Louis captain said.
Backes has four goals and five points in the past four games. The overtime goal was the first of his career.
The Blues (22-6-3) spotted the Blue Jackets a 3-1 lead in a frenetic first period, overcame a series of penalties to trail by a goal after two, and rallied late to tie the game.
McKenna, a St. Louis native who was making his first NHL start in more than three years, finished with 27 saves. St. Louis' Jaroslav Halak stopped 30 of 33 shots to pick up the win.
McKenna said he didn't get a good read on what Backes was doing with the puck before the goal.
"As soon as he made a move with his backhand, I went hard to the other side and the puck went back across, and I'm dead in the water," McKenna said. "It's frustrating. We were right there and definitely played well enough to win."
Chris Stewart tied the game at 3-3 with 6:27 left in regulation, 20 seconds after Columbus forward Mark Letestu shot over the Blues net on a breakaway. Stewart was in position for a rebound after a shot from the left point by Ian Cole was tipped in front by Brenden Morrow.
Vladimir Tarasenko scored the Blues' first two goals. Anisimov, Tyutin and Ryan Johansen had goals for Columbus, which had been 36-0-0 when leading after two periods under coach Todd Richards since Jan. 9, 2012.
"[The media] were making a lot out of that," he said. "I still don't mind the way we played in the third period. The effort, the competitiveness for the most part was where it needed to be."
McKenna, who relieved Curtis McElhinney for the final two periods Thursday in a 4-2 win against the New York Rangers, had not started an NHL game since Nov. 20, 2010, when he played the Blues as a member of the New Jersey Devils. He is 4-9-1 in 19 NHL games and is still looking for his first victory since making 33 saves for the Tampa Bay Lightning in a 2-1 overtime win against the Blue Jackets on March 24, 2009.
St. Louis improved to 9-4-1 on the road while Columbus' four-game win streak in Nationwide Arena came to an end.
Columbus (14-15-4) fell behind 1-0 on Tarasenko's first goal, but came back with goals from Anisimov, Tyutin and a 5-on-3 goal by Johansen for the lead after 20 minutes.
Along the way, there were four fighting majors, three roughing calls and a late unsportsmanlike conduct to Backes.
St. Louis went in front at 4:10 when Jay Bouwmeester's shot caromed off the traffic in front to Tarasenko, who put the puck off McKenna and into the net.
Columbus tied it when Anisimov scored for the second straight game, converting a centering pass from Blake Comeau at 8:49 after getting position on Bouwmeester in the slot.
Less than three minutes later, the Blue Jackets' forechecking paid off when St. Louis defenseman Alex Pietrangelo, under pressure, sent his clearing pass to Tyutin's stick. The Columbus defenseman let a shot go from the left point that went off Halak's glove and into the goal.
The game got even more interesting during an ensuing Columbus power play when Matt Calvert dumped Blues defenseman Barret Jackman. After the penalties were sorted out, Cole received an extra two minutes for roughing, and seven seconds into the two-man advantage, Brandon Dubinsky fed Johansen cross-ice for the one-timer from the lower left circle for 3-1 lead at 13:27.
Johansen has four goals and 10 points during an eight-game point streak.
"I like the way we responded after their goal," Richard said. "There was no panic on the bench."
Tarasenko made it 3-2 at 8:33 of the second period with a slap shot from the left side with Columbus down a man.
"We made it hard on ourselves," Backes said. "The two previous games we played the right way, not that it was easy but it was the right way for 60 minutes."