Joe Thornton's power-play goal tied it at 2 in the final period, after Swedish-born Kristian Huselius had thrilled the crowd when he scored his second goal of the season on a power play to put the Blue Jackets up 2-1 at the start of the third.
"It was nice to bounce back and get the win here," Huselius said.
San Jose took the lead with a power-play goal from Devin Setoguchi 2:02 into the first period.
"I think it's safe to say that he's [Mason] probably got his game back to where it was two years ago," said Columbus coach Scott Arniel. "Last night he got off to a slow start but he was outstanding from that second period on, and tonight all three periods."
San Jose won Friday's game 3-2.
There were a lot more empty seats at the 13,500-capacity Globen Arena compared to Friday, probably due more to high ticket prices than an apathetic Swedish public.
"I guess it was more fans here the first game but it felt like it was more noise and they were more into the game tonight," said Huselius. "We had some good times here."
Like in the first game, the frantic start was followed by a cagey second period with neither team able to add to the score.
As well as being the Blue Jackets' first win of the season, it was also coach Arniel's first in the NHL.
"I didn't want this to drag on," Arniel said. "The longer it goes on you start to worry and wonder when it's going to come but certainly in that dramatic fashion tonight, we had a pretty happy bench and a pretty big group hug behind the bench after Ethan scored."
San Jose hit the post twice in the second period with the score at 2-2.
"I didn't think we were very competitive early in the game," said San Jose coach Todd McLellan. "It's been a long trip."
McLellan added that he has a better idea of what the team needs to improve on.
"At least we have a measuring tool, we know where we're at, we have some points in the bank that people can't take away from us and we start building on our season," McLellan said.
The teams' next matches will be back on more familiar territory. Columbus hosts Stanley Cup-holder Chicago next Friday and San Jose plays Atlanta a day later.