Giordano, who had played his entire 15-season career with the Flames after signing as an undrafted free agent in 2004, was claimed by the Kraken in the 2021 NHL Expansion Draft on July 21.
The 37-year-old defenseman gave Seattle a 1-0 lead at 3:00 of the first period.
"It's been good," Giordano told Root Sports Northwest during the first intermission. "Surprisingly I felt pretty calm. I think just maybe before the game a little bit of nerves seeing the guys in warmup and stuff like that. But felt pretty calm, feel good, glad I did this in [an] exhibition."
Giordano, who had been Calgary's captain since the start of the 2013-14 season, scored 509 points (143 goals, 366 assists) in 949 regular-season games with the Flames, including 26 points (nine goals, 17 assists) in 56 games last season, and has scored seven points (one goal, six assists) in 23 Stanley Cup Playoff games.
He led Calgary in ice time per game in seven of the past eight seasons, including last season, when he averaged 22:57.
"I've developed so many relationships. I grew up as an adult here," Giordano said. "The thing that I would want them to remember me as, playing well or playing poorly, I gave it my all every shift and every night and I'll continue to do that. That's one thing I hope they remember me as.
"I have so many different memories of this city and good times on and off the ice. It's a special place, obviously, for my family and I. A lot of great people. I've developed relationships in this city, for sure."