The Coyotes squandered a two-goal, first-period lead but won for the fourth straight time against the Flames at home.
Mike Smith made 30 saves, helping Phoenix in its push for a playoff spot. The win gave the Coyotes 75 points, tying them with Dallas. The Stars, however, maintained their hold on the second wild-card spot in the Western Conference because they have played two fewer games.
Mike Cammalleri assisted on both power-play goals Calgary scored in the second period.
Joni Ortio stopped 22 shots for the Flames.