The defending champions beat Japan 2-1 after extra time in steamy Cibinong, West Java as Lee Seung-woo and Hwang Hee-chan scored the goals that will allow 26-year-old Son to see out his new five-year deal with Spurs.
A late header from Ayase Ueda gave South Korea an almighty fright, but they saw out a nervous last few moments to win a record fifth Asian Games title.
Korean captain Son, substituted in the dying seconds to buy precious time, sprinted from the bench to embrace goalkeeper Jo Hyeon-woo, sobbing tears of joy as they rolled on the turf together.
The Koreans dominated the final but wasted several decent opportunities before substitute Lee broke the deadlock by smashing a left-foot shot into the roof of the net three minutes into extra time.
Son delivered a free kick for Hwang to ram home a towering header eight minutes later, before Ueda's goal triggered late drama.
South Korea could have been three goals up by halftime, with Lee Jin-hyun blazing just over from distance and Son bundled over in the box for what replays suggested was a clear penalty.
Hwang Ui-jo went close as the Japan-based striker went in search of his 10th goal of the tournament before Japan captain Koji Miyoshi forced a sharp save from Jo.
Roared on by thousands of flag-waving "Red Devils" fans, the Koreans continued to press as Hwang rippled the side-netting just after the hour mark but both sides wilted in the sapping conditions as the game went on.
Failure to win gold could have been disastrous for Son's career as the multi-millionaire footballer faced swapping his tracksuit for a camouflage kit and 21 months of national service, compulsory for South Korean men.
Spurs only released their forward to compete as one of three permitted over-age players at the far-flung, regional under-23 tournament because he pleaded with the London club.
Nearly every able-bodied South Korean male is required to perform their military service before the age of 28, although the government rewards Asian Games gold medals and Olympic medals of any colour with an exemption.
Son was selected to play at the 2014 Asian Games but his former club Bayer Leverkusen refused to release him -- and the Koreans scooped gold.
His tears after South Korea's quarter-final defeat by Honduras at the 2016 Rio Olympics melted hearts, and thousands offered to do double their own military service in an online petition if Son could be pardoned.AFP