Son won the penalty from which Hwang Ui-jo opened the scoring after 14 minutes and provided the corner for Kim Min-jae to double the lead early in the second half.
It was a deserved win for Paulo Bento's side, who looked a far more convincing outfit with Son in their starting XI and his arrival should offer hope of a run into the latter stages of a tournament they have not won since 1960.
Korea will now face the best third-placed team from Group A, B or F, while Marcello Lippi's men – who would have topped the group with a point – have a last-16 date with Thailand.
Hwang had already been denied one-on-one and Kim put a free header wide by the time Son drew a foul in the area with Zheng Zhi and Shi Ke having a nibble at the Tottenham forward.
The spot-kick was clinically dispatched into the bottom-left corner by Hwang and only the far post cruelly denied his brilliant curling effort from the left of the box making it 2-0.
It was essentially game over by the 51st minute when Kim emphatically headed home Son's left-side corner at the near post.
Kim Moon-hwan was unfortunate to see an edge-of-the-box shot bend wide after a jinking run, while Kim Jin-su and Hwang Hee-chan also went close to adding what would have been a deserved third.