The Flames goalie played the whole game, finishing with 18 saves on the 21 shots he faced.
Tkachuk, Michael Stone and Mikael Backlund scored for Calgary in regulation.
Giordano - who was cheered on by the homecrowd to start the tilt - broke his stick on his shootout attempt but made good earlier in the night.
He scored exactly three minutes into the tilt, taking a pass from McCann as he skated in from the blueline and scored with a backhand through the five-hole of Vladar. The crowd gave him a warm ovation after.
The line of Tkachuk and newcomer Blake Coleman flanking Elias Lindholm started, with Noah Hanifin and Chris Tanev on defence. It was the first preseason action for the five.
That forward trio wasted little time getting the crowd out of their seats, Tkachuk skating over the blueline and feeding a pass through two defenders to a streaking Coleman, who pulled the puck to his backhand as he skated across the crease but put his offering up-and-over the net.
After Giordano's goal, the visitors made it 2-0 just past the six-minute mark when Vladar made the intitial stop on a point blast from Adam Larsson, but Jaden Schwartz was in the perfect spot to grab the rebound and put it in the open net.
Tkachuk got the Flames on the board with 5:06 left in the opening frame, cashing in on a pass from behind the net courtesy of Lindholm, No. 19 putting an in-tight backhand into the far top corner.
Coleman also collected a helper on the marker.