Jonathan Bernier made 32 saves for the defending Stanley Cup champions, who tied it with 9:34 left on Jeff Carter's goal during a two-man advantage. King then made a spinning pass from the boards in front to Kopitar, who beat Jimmy Howard for his sixth goal of the season.
Howard stopped 27 shots for the Red Wings, who had won two straight after an 0-3-2 skid.
Kyle Quincey scored his first goal of the season on a misplay by Bernier in the first period.
It was definitely emotional. I really appreciated the fans. It was a cool feeling and it felt special and the ovation there at the start and then you kind of feel funny out there standing by yourself. Thinking back, I was saying just a bit ago, you think back just trying to make the NHL and then you kind of reflect on all the years being able to play for a great organization here in Calgary and all the fun I've had so far in my career. I feel very fortunate and blessed.
— Boston forward Jarome Iginla on his return to Calgary, where he played for 16 seasons