Matt Calvert failed to score on the first attempt in the second period and Vermette missed with a chance to tie it midway through the third.
"There's nothing you can do," Kiprusoff said. "You just have to make sure you stop it."
It's the first time a goalie has turned aside two penalty shots in an NHL game since Detroit's Corrado Micalef stopped Pierre Larouche and Mike Ridley of the New York Rangers on Feb. 16, 1986.
"That's definitely not history you want to be a part of," Calvert said. "He got me on that one. I was trying to go shelf and trying to get him to move, but he read it pretty good and stayed in one spot and I didn't have much to shoot at."
The Flames jumped from a tie for seventh place to fifth alone in the congested Western Conference standings. They are 14-3-3 in their last 20 games.
Jarome Iginla and Olli Jokinen scored first-period goals for Calgary. Iginla has 29 goals in his bid to become the 10th NHL player to score at least 30 goals in 10 seasons. Glencross also had two assists.
Kiprusoff, making his 19th straight start, finished with 37 saves for his 30th victory.
"He gives us a chance to win every night," Jokinen said. "You can see how focused he is every day. He's the biggest reason we've been winning games."
The Blue Jackets have failed to score on five penalty shots this season, four in the last five games.
"You get that many penalty shots like we have in the last little stretch here, you'd think sooner or later the odds are that you're going to score on it," Columbus coach Scott Arniel said.
Trailing 4-2 after two periods, the Blue Jackets outshot the Flames 16-4 in the final frame.
"If you're going to try and make it to the next level and get to the playoffs, you have to find a way to beat these guys and we had more than our share of opportunities to equal that game tonight," Arniel said. "We peppered them pretty good in the third."
Craig Rivet opened the scoring for Columbus in the first and Vermette tied it in the second before taking the costly penalty. Jan Hejda cut it to 3-2 early in the third.
Columbus has lost four straight, all on the road, to fall to 12th in the West.
Columbus goalie Steve Mason made 24 saves.
The Flames went on the key extended power play when Vermette high-sticked David Moss.
"Obviously, it's an accident," Vermette said. "This time of year, it makes a difference -- penalty killing and power play -- and they capitalized on that."
After Bourque backhanded a rebound past Mason to put Calgary up 3-2, Glencross tipped in a point shot.
Calvert was awarded his penalty when he was hauled down from behind by defenseman Mark Giordano, but Kiprusoff made a blocker save to keep the Flames up by a pair heading to the third.
Columbus made it 4-3 at 6:43 of the final period when Hejda blasted a point shot through traffic into the top corner behind Kiprusoff.
Vermette had a chance to tie it when he was awarded his penalty shot after Anton Babchuk was ruled to have thrown his stick trying to break up the play. Kiprusoff made stopped Vermette with his left arm.
"He made two great saves on two penalty shots," Glencross said. "Kipper stuck in there for us and played another great game."
- With Brendan Morrison (knee) and Mikael Backlund (flu) out of the lineup, trade-deadline acquisitions Fredrik Modin and Brett Carson made their Flames debuts.
- Columbus forward Samuel Pahlsson played in his 700th regular-season game.