The win redeemed Kiprusoff, the Flames' goalie who allowed 10 goals in his last 51 shots entering the game.
"Feels good to come up with a win," Kiprusoff said. "We played a smart game, and a very good road game. We lost two in a row and can't lose three straight."
Coach Mike Keenan pulled Kiprusoff after the second period in the Flames' 4-2 loss to the Ducks on Sunday night. In his previous game against the Kings, Kiprusoff allowed six goals in a 6-3 loss. He was much better against the Coyotes, earning his 30th win of the season.
The win also ended Phoenix's three-game winning streak.
"From start to finish, this was a more consistent performance," Keenan said. "In December and January, we were not consistent and we need to rekindle the consistency here in the final weeks of the season."
Iginla opened the scoring when he tipped in Adrian Aucoin's shot from the left point at 3:52 of the second period. He later hit an empty net at 19:26 of the final period for his 37th of the season, two shy of his total from last season.
In playing a strong checking game, the Flames limited Phoenix's chances and created opportunities.
"This is type of game we have to play," Iginla said. "The forwards came back, the defense stood up in front and [Kiprusoff] played well. We need to play this way from here on out."
Phoenix tied it when defenseman Derek Morris drilled a slap shot past Kiprusoff for a power-play goal at 6:51 of the second period.
Calgary regained the lead 30 seconds later as Phaneuf scored his first of the game on the power play.
Phaneuf picked up his second goal when he sent a slap shot from the left point at 2:32 of the third period into the Phoenix net.
Through a scoreless opening period, Phoenix had the best opportunity. That's when defenseman Keith Yandle's point-blank shot, from 15 feet, was gloved by Kiprusoff midway through the period.
Phoenix coach Wayne Gretzky offered a contrast to the Flames' ability to raise its emotional level and the response by his Coyotes.
"They played like this was a playoff game and we played like it was a September exhibition game," Gretzky said. "They beat us to every loose puck. They took hits to make plays and we showed no grit. We only had a handful players who showed up."
Phoenix rookie center Martin Hanzal missed his eighth straight game because of a shoulder injury. ... The game was the fourth of a five-game Calgary road trip, their second longest this season. ... Doan's assist on the Coyotes' goal was the 315th of his NHL career, fourth all-time on the Winnipeg/Phoenix franchise list. ... Iginla's
three-point game was his first since Jan. 5 against the Kings.