Spoelstra shared the story before Wade's final regular-season Heat home game Tuesday at AmericanAirlines Arena in Miami.
The 13-time All-Star and three-time NBA champion will hang up his jersey Wednesday. His No. 3 will soon be raised to the rafters of AmericanAirlines Arena, alongside the threads of fellow franchise legends.
"I will never forget the game winner he hit in 2004 against the Utah Jazz," Spoelstra said. "After he hit that game-winner and the celebration in the arena, I went back in the locker room. After it all died down he came back after the media session and hugged me and thanked me."
"I have never forgotten that because I had nothing to do with that. But I tell you what, 15 years later I've been doing everything I possibly could do to reward him ... everything I can to earn all that he has done for this organization."
Spoelstra was a Heat assistant at the time of the shot, but considered himself the guy who shagged balls for Wade. He helped Wade work on his mid-range game at the time, but refuses to believe he had much to do with Wade's brilliance.
Spoelstra became the team's head coach in 2008, leading the franchise to back-to-back NBA Finals victories in 2012 and 2013.
While Wade will walk away from the game after the Heat's regular-season finale against the Brooklyn Nets, Spoelstra still holds out hope that the franchise icon will return to AmericanAirlines Arena in a different capacity.
"I am very hopeful that he will be around a lot later on," Spoelstra said. "I think he will want to. I will always leave a spot open for him as honorary coach, but he is too smart to take that. Whatever the role is, I am sure he will do it and there is no better ambassador than him for this organization."
The future Hall of Famer takes the NBA court for the last time at 8 p.m. Wednesday in Brooklyn.