"As a coach, you go in and challenge your group," coach Todd Richards said. "There were some questions I had coming out of the Edmonton game. To me, they responded the right way."
After Artem Anisimov was stopped by Calgary goalie Reto Berra, the puck came to David Savard, who had a shot blocked by Mikael Backlund. However, the puck caromed out to Nikitin, who had an empty net with Berra down and out.
"Nikita, as far as the way he played, it might have been his best game," said Richards, who was pleased with the entire team's performance. "They came out and they played hard. Ran out of gas a little bit toward the end.
"I thought we battled. We got the win. The way they are playing out on the ice, I think the attitude is real positive."
After the winning goal, the Flames' first-year goalie repeatedly pounded his glove into the ice.
"It was great how we came back, but at the end it was bad luck," said Berra, who had 16 saves in falling to 2-4-2.
Nick Foligno also scored for Columbus (8-11-3). The Blue Jackets are 2-1 with two stops left on a five-game road trip.
"We just had too many mental lapses last night and it cost us," Blue Jackets center Ryan Johansen said. "It's nice to be able to forget about that now. Coming in here and doing all those little things right in our defensive zone."
Joe Colborne scored for Calgary (7-11-4), which has lost six straight at home (0-5-1).
The Flames were coming off a 5-4 shootout victory in Winnipeg on Monday. They were trying to win two games in a row for the first time in over five weeks.
"I don't think it was the most exciting game, especially when they scored early. I think they would have been happy to go home with a 1-0 road win," Flames coach Bob Hartley said. "The bottom line is it's pretty tough to win when you only have one line going.
"Matt Stajan's line was by far our best line, and we didn't get enough from the other three."
The Blue Jackets were looking to rebound from a 7-0 rout in Edmonton on Tuesday. Columbus was a lot tighter defensively against the Flames, limiting their scoring chances until Calgary tied it 3:28 into the third period.
Kris Russell found David Jones near center ice with a long breakout pass. As the Blue Jackets rushed toward him, Jones neatly left the puck for Colborne, who raced past flat-footed Jack Johnson. Colborne took off on a breakaway and tucked a backhander over Bobrovsky's shoulder.
"To have a chance to play right away, to reset, it's good," said Bobrovsky, who was pulled against Edmonton after the fourth goal. "You don't think about the game before. It was a bad game. You have a chance to win and you get that good feeling again."
Bobrovsky wasn't overly busy against Calgary but he made the stops he needed to and finished with 23 saves. After winning the Vezina Trophy last season as the NHL's best goalie, Bobrovsky hasn't had nearly the same success this season, going 7-9-2.
Berra made his eighth start in nine games for the Flames and made 16 stops in falling to 2-5-1.
Columbus took a 1-0 lead in the first period.
Foligno's slap shot deflected off the leg of Flames defenseman TJ Brodie, and the sudden change in direction sent the puck into the top corner of the net behind Berra.
The Blue Jackets were without C Brandon Dubinsky, who sustained a bruised foot against Edmonton. Recently recalled RW Jack Skille took his spot in the lineup. ... Columbus LW Matt Calvert (lower body) is back practicing and could return Friday. He has missed 19 games. ... Bobrovsky has given up at least four goals six times this season. That happened only five times last season. ... Calgary is 6-3-4 in one-goal games.