The four-point performance tied a career best for Iginla, who also had four points against Phoenix on Feb. 23, 2003.
The Flames took the lead in the opening period. Iginla knocked in a rebound of a Dion Phaneuf shot from the left point at 18:21.
The Flames increased their lead to 2-0 early in the middle period when Alex Tanguay fired into an open net with Phoenix goal Mikael Tellqvist out of position.
Phoenix answered with two goals within 3 1/2 minutes.
Defender Keith Ballard carried the puck in behind the Calgary net and slid a pass out in front. A trailing Ladislav Nagy shot the puck past Miikka Kiprusoff at 4:28. Mike Comrie lifted in a rebound at 8:01 to tie the game.
The Flames regained the lead when Daymond Langkow scored on a power-play goal, grabbing a rebound from Richie Regehr’s shot from the right point at 10:06. On the play, Tellqvist lost his stick and was caught in a tangle of players in front of the Coyotes net.
Iginla added his second tally of the game, and 20th of the season, with a two man advantage when he fired in a 20-foot wrist shot from the slot at 7:12 of the final period.
The Coyotes drew within one at 4-3 when Travis Roche crashed the slot, knocking in a drive off the stick of Oleg Saprykin at 14:55 for his first NHL goal.
Calgary responded when Bryon Ritchie drove in a rebound at 15:50.
Iginla’s second assist came on an empty-net goal from the Flames’ Tony Amonte in the final minute.
It was the fourth loss in the last five games for Phoenix.
Notes: Day-to-day with a groin strain, Phoenix goalie Curtis Joseph is two wins behind Jacques Plante for fifth place all time with 435. Just ahead is Terry Sawchuk with 447. … Attendance was listed as 15,551, and the Coyotes have not sold out a home game this season.