Giordano's goal was a big one, extending the Flames lead to 3-1 at 11:46 of the second period. On the power play, Giordano's shot from the blue-line changed direction off the stick of Antoine Vermette and eluded goaltender Thomas Greiss.
Calgary has been without its captain since he sustained the injury Oct. 21 in a win in Los Angeles. At the time, the Flames were 4-2-2. While he was absent, the club struggled going just 5-11-2.
TJ Brodie, Mikael Backlund and Lee Stempniak also scored for Calgary (10-13-4). The Flames have won consecutive games for the first time since Oct. 9 and 11 and won on home ice for just the second time in their last nine tries (2-5-2).
Keith Yandle scored the lone goal for Phoenix (16-8-4), who had won 6-2 in Edmonton on Tuesday night. The Coyotes have split the opening two games of their four-game road trip, which continues Friday night in Vancouver.
Trailing 1-0, the Flames got an important goal with eight seconds left in the first period when Brodie's shot deflected in off the leg of Phoenix defenceman David Schlemko. The third goal for Brodie is a new career high.
The goal enabled Calgary to head to the dressing room even despite being outshot 11-3 in the opening 20 minutes.
The Flames played a much better second period, taking the lead at 5:48 when Backlund ended an 18-game scoreless drought with a knuckler off a one-timer after being set up on a nifty cross-ice feed from Jiri Hudler.
Up 3-1 heading to the third period, Calgary got insurance at 2:44 in the form of their league-leading sixth short-handed goal.
Matt Stajan led a two-on-one rush and after showing tremendous patience, eventually slid a pass across to Stempniak who buried his fifth goal of the year in the open side. It was the first goal in 10 games for the veteran since he returned from missing seven games with a broken foot.
The benefactor of all the offence was Karri Ramo. Making his second consecutive start after stopping 21-of-22 shots to beat Los Angeles on the weekend, the 27-year-old Finn was excellent again finishing with 29 saves to improve to 4-4-1.
In the pivotal second period when Calgary bolted into the lead, Ramo had a pair of solid glove saves — first denying Vermette, and in the final minute robbing Mikael Boedker.
With Mike Smith getting the night off, Greiss made his fourth start. He had 14 saves to fall to 3-2-0.
Notes: Phoenix fell to 12-2-1 when they score first ... The Flames won by more than one goal for just the second time. They entered the night 1-9-0 in goals decided by two or more goals ... Calgary was coming off its fifth break of three or more days. Excluding the Olympic break, they have just two more breaks of that length the rest of the season ... Phoenix's Radim Vrbata saw his five-game points streak come to an end ... Sven Baertschi returned to the Flames' line-up after being scratched the previous game.