The Czechs briefly thought they had regained control when they found the net again, only for the effort to be ruled out.
Hwang then turned provider, delivering a cross from the right that Oh Hyeon-gyu converted in the 80th minute to complete the comeback and hand South Korea all three points.
Captain Son Heung-min, who was repeatedly denied despite an energetic display, sank to the turf in celebration after the final whistle.
South Korea will next face co-hosts Mexico, who opened Group A with a 2-0 win over South Africa, while the Czech Republic take on South Africa in their second group match.
