Curtis Glencross and Mikael Backlund combined to set up Giordano just inside the blue-line and with Mike Smith screened on the play, Giordano put a shot just inside the goal post. Afterwards, Smith just shrugged his shoulder as if he didn't see the puck at all.
Jiri Hudler and Lee Stempniak also scored for Calgary (15-21-4). The Flames, who had lost six of their last seven, snap a three-game losing streak at the Scotiabank Saddledome.
In the overall standings, Calgary pulls even with the reeling Carolina Hurricanes, two points ahead of the Florida Panthers and Colorado Avalanche, who are tied for last.
Antoine Vermette and Keith Yandle scored for Phoenix (18-16-7). The Coyotes pick up three out of six points on their three-game road trip.
It was a costly loss for Phoenix which now finds itself in a three-way tie for ninth in the Western Conference, joined by Dallas and Columbus who both won on Friday. They are two points behind the Detroit Red Wings, who occupy the eighth and final playoff spot.
Although Phoenix outshot Calgary 11-2 in the third period, they hadn't had a dangerous scoring chance until Yandle took a diagonal pass from former Flame Derek Morris and one-timed a rocket from the face-off circle that beat Joey MacDonald over his glove to tie the game 2-2.
Stempniak put the Flames ahead 2-1 at 18:52 of the second period, scoring on a power play.
TJ Brodie's slap shot was partially stopped by Smith but the puck trickled through and Stempniak raced to the net, poking the puck over the line for his first goal in 15 games..
Phoenix opened the scoring 1:29 into the game, before many in the announced sell-out crowd of 19,289 had settled into their seat. Vermette got his own rebound and from the top of the crease, put his 10th of the season past MacDonald.
Calgary tied it 1-1 in the final minute of the first. From behind the net, Mikael Backlund centred the puck and it caromed off the skate of Hudler and behind Smith.
It was the eighth goal of the season for Hudler, who was back in the line-up after missing two games with an upper body injury.
Phoenix nearly took the lead in the second when Mikael Bodker's slap shot off the wing was stopped and Alexandre Bolduc, driving to the net from the office side, was robbed on the rebound as MacDonald scrambled across. Bolduc slammed his stick into the boards in disbelief afterwards.
MacDonald finished with 29 saves, Smith had 22 stops.
Smith made his fourth start in a row after returning from an upper body injury. He entered the night having stopped 93 of 95 shots in his previous three appearances.
Calgary lost veteran left-winger Alex Tanguay 6:42 into the second period when his knee buckled under him while battling for puck in the Coyotes end. He was helped off the ice and was not putting weight on his left leg.
Notes: Prior to the game, Calgary announced the signing of Ben Hanowski to a two-year entry level contract. Hanowski, 22, was acquired from Pittsburgh in the Jarome Iginla trade. His NCAA career just concluded when St. Cloud State lost Thursday in the semi-final of the Frozen Four… Dennis Wideman picked up his 200th career assist on Stempniak's goal… Phoenix D Rostislav Klesla was a healthy scratch… Smith is two shutouts away from tying Bob Essensa and Sean Burke (15) for third on the franchise career shutouts list.