Iginla paced Calgary with a goal and two assists, but said Kiprusoff bailed out the Flames early.
"We have so much confidence in him," Iginla said. "We haven't been playing as tight in front of him as we should, but he makes huge, timely saves. Those get forgotten at times as the game goes on."
Smyth advanced on Kiprusoff with a clear-cut breakaway, but the Flames' goalie made a pair of pad saves before covering up the rebound.
"It's a nice way to start the game if you stop that," said Kiprusoff, who finished with 22 saves to improve to 18-13-3. "The puck was bouncing a little bit and he just tried to shoot quickly and I was able to stop that."
Daymond Langkow also scored for the Flames, and praised the reigning Vezina Trophy winner.
"That's probably the turning point in the game right there," Langkow said.
Smyth went on to score both Oilers goals, but regretted missing those early chances.
"Obviously, I'd love to have that one back and capitalize on the chances like that early on in the game," the Edmonton captain said. "Off of that, it gave them a little momentum and they capitalized on the first one and from there the rest is history."
Dion Phaneuf and Chuck Kobasew also scored to help the Flames win their second straight on their current six-game homestand.
Jarrett Stoll had two assists for the Oilers, losers of four straight.
"We've got to fight and battle out of this," said Edmonton goalie Dwayne Roloson, who made 20 saves. "We've all got to stick together and do the little things that win hockey games."
Smyth said he believes the Oilers can begin to turn their season around on Tuesday night when they return home to face the Florida Panthers.
"We've got to stay focused," he said. "We believe we're a good hockey team and once we believe that and start playing with confidence, we'll eventually find a way through it."
Calgary jumped out to a 1-0 lead at 5:48 of the first when Kristian Huselius spotted Iginla in the slot and feathered him a nice pass. The Calgary captain wired a one-timer past Roloson, who was screened by defenseman Jason Smith.
Less than 4 minutes later, Iginla fought with Roloson for the puck behind the Oilers' net and came away with it, centering a pass that Langkow deposited it into an empty net to put the Flames up 2-0.
Just 49 seconds into the second period, Phaneuf wristed a point shot past Roloson, who was screened by Langkow, during a Calgary power play.
The Oilers then responded on a man advantage when Smyth tipped a point shot by Daniel Tjarnqvist into the top corner past Kiprusoff.
The Flames regained their three-goal lead at 3:53 of the middle frame when Alex Tanguay spotted a streaking Kobasew and hit him with a perfect pass in front of the Edmonton net. Kobasew swatted it past Roloson for his first goal in 13 games.
"He sees the ice so well," Kobasew said of Tanguay. "As soon as I saw him go into the corner looking over his shoulder, I knew to go back ... and he put it though some traffic to make it."
In the third, Smyth redirected a pass from Stoll past Kiprusoff during a two-man advantage for the Oilers to narrow the deficit to two goals.
Notes: Calgary defenseman Roman Hamrlik returned to the lineup after missing seven games with a groin injury. During that span the Flames were 3-3-1. ... Heading into the game, the Oilers were ranked first in road penalty killing with a 93.7 percent efficiency rate having allowed just six power-play goals in 95 short-handed situations.