Roman Hamrlik led the way with a goal and an assist, while Daymond Langkow added a pair of helpers. Chuck Kobasew, Kristian Huselius, Tony Amonte, Jarome Iginla and Marcus Nilson also scored for the Flames, who halted a three-game losing streak in front of 19,289 fans at Pengrowth Saddledome.
Miikka Kiprusoff stopped 26 of 27 shots to improve his record to 3-4-1. Last year's Vezina Trophy and Jennings Trophy winner has played all eight games for Calgary so far this season.
Owen Nolan scored the lone goal for the Coyotes (2-8-0), who also lost 5-2 Monday night in Edmonton to the Oilers. The Coyotes have now lost four straight and are in last place in the Western Conference.
The Flames killed off three first-period power-play opportunities for Phoenix, including a two-man advantage that lasted 42 seconds. Kiprusoff made a pair of nice saves off point shots fired by defenceman Ed Jovanovski to keep the game scoreless.
Calgary opened the scoring on a two-man advantage of their own. Kobasew took a pass from Jamie Lundmark and quickly shovelled the puck past Phoenix netminder Mike Morrison at 14:41 of the first period.
Just 65 seconds later, Huselius scored his first of the season on another power play when he kicked the puck onto his stick and swatted it past Morrison.
Nolan replied for Phoenix before the end of the period when he backhanded a shot over Kiprusoff's shoulder and into the top corner.
Amonte scored short-handed in the second period when he pounced on a turnover in the neutral zone and sped into the Phoenix territory before sending a wrist shot past Morrison, who was subsequently replaced in goal by Curtis Joseph.
Kiprusoff made back-to-back pad saves off Phoenix forward Enver Lisin in the final minute of the second period to preserve Calgary's two-goal lead.
Iginla opened scoring in the third with a perfect shot into the top corner past Joseph. Nilson's goal followed when he converted a feed from Lombardi to make the score 5-1. Hamrlik rounded out the scoring with his first goal of the season on another Calgary man advantage.
Daymond Langkow had a great chance to add to Calgary's lead, but his penalty shot attempt in the third hit the left post behind Joseph.
The Flames finished 3-for-10 on the man advantage, while the Coyotes failed to score on nine power-play opportunities.
Notes: Kiprusoff started the season off last year with a 2-4-1 record as well before he backstopped the Flames to a 3-1 win over the Edmonton Oilers on home ice on Oct. 20, 2005. He went on to win eight games in a row and finished the season with a 42-10-11 record and 2.07 goals against average. . . . Phoenix centre Mike Zigomanis, who has won 59.6 per cent of his faceoffs to rank third in the NHL so far this season, missed the game with a groin injury he suffered during the loss to Edmonton. . . . The Flames improved their all-time record over the Coyotes/Winnipeg Jets franchise to 66-57-22.