A late response by Japan's Ayase Ueda caused jangling nerves but Korea held out and the 20 members of their squad are now spared otherwise compulsory military service on grounds of sporting excellence.
"I've got the gold medal around my neck but it really belongs to the Korean people", he said.
"I still believe that we could have gotten a gold medal if we had enough practice time", Park, the WNBA star, said through an interpreter.
He could have earned exemption at the 2014 Asian Games when South Korea won gold, but Bayer Leverkusen - his club at the time - refused to let him join up with his country.
Almost every able-bodied South Korean male is required to perform military service before the age of 28, although the government rewards Asian Games gold medals and Olympic medals of any colour with an exemption.
The dam finally broke a few minutes into extra-time as substitute Lee Seung-woo of Hellas Verona collected a pass from Son and rocketed the ball into the top corner.
Spurs only released their forward to compete as one of three permitted over-age players at the far-flung, under-23 tournament because he pleaded with the London club. And when I see the people, the way they support me, I want to give something back. On Saturday, Son and South Korea beat Japan 2-1 to claim the gold medal. "We just trained as a combined team for a month".
And China also went home with all five table tennis gold medals as Fan Zhendong won the men's singles and Wang Manyu won the women's - both against Chinese opposition.
"The team comprises good men and quality players".
Son's career-saving gold was the highlight of a busy final full day of competition, with 44 gold medals in play as Sunday's closing ceremony looms. In the 3rd-place playoff, Chinese Taipei defeated Qatar 3-1.