The East Asian country’s other Premier League player, Hwang Hee-chan of Wolverhampton Wanderers, scored South Korea’s other goal at the Daejeon World Cup Stadium.
South Korea survived some dicey moments early on, turning the ball over deep in their own zone as Chile pressed forward.
But Hwang broke through on 12 minutes, with a well-struck right-footer finding the top right corner past Fernando de Paul.
Chile then fought back with a few dangerous chances past the half-hour mark. Marcelino Nunez and Diego Valencia each just missed the net with close-range attempts.
Just before halftime, Benjamin Brereton Diaz nearly levelled with a low shot that rolled wide of the left post.
Chile failed to build on that momentum in the second half, with defender Alex Ibacache sent off following a second yellow card on 52 minutes.
Despite being a man down, the visitors pushed hard for an equaliser, with a Brereton Diaz header nullified by an offside call at the hour mark.
Son almost doubled South Korea’s lead on 66 minutes but his low left-footed attempt from the left side of the box rolled just wide of the far post.
Seven minutes later, Brereton Diaz tried to respond for Chile, but his promising foray into the box only resulted in a weak shot turned aside by Kim Seung-gyu.
Son, the 16th South Korean to hit the century mark in international caps, eventually gave the 42,000 fans something to cheer about with a gorgeous free kick from just outside the box to seal the win.