Thapelo Maseko scored mid way through the second half against South Korea to take South Africa into the knockout stages at a World Cup for the first time.
The 22-year-old drove a fierce shot past the South Korean goalkeeper Kim Seung-gyu after 63 minutes at the Monterrey Stadium on Wednesday night.
South Africa came under sustained pressure from the South Koreans who started the day in second place.
But Hugo Broos's men held firm to book a last 32 showdown with co-hosts Canada in Los Angeles on 29 June.
"We scored that goal, and it was 20 minutes of my heart beating and hoping that the game should be finished as soon as possible," said Broos.
The 74-year-old Belgian added: "So yes, we are in the second round. It's historic. I'm very happy for the guys. I've worked with them for five years. And what we did in those five years is amazing."
The victory gave South Africa four points to finish second behind Mexico who completed a clean sweep of their Group A matches with a 3-0 win over Czech Republic.
The Czechs leave the tournament with one point - a draw with South Africa - from their three games.
South Korea, who have three points, must wait to see if they move into the knockout rounds as one of the eight best third-placed teams.
Switzerland win Group B
In the final round of games in Group B, Switzerland saw off Canada 2-1 in Vancouver to claim top spot ahead of their opponents.
Bosnia and Herzegovina overcame Qatar 3-1 in Seattle. With four points from their three matches, they will be among the leading contenders for a place in the last 32 as one of the best third-placed teams.
Brazil sweep past Scotland
Brazil won Group C. They romped past Scotland 3-0 in Miami to finish with seven points - the same tally as Morocco - but ahead on goal difference.
"I'm gutted with the result," said Scotland midfielder John McGinn. "We gave away goals at bad times against a team that can punish you with quality.
"We were short on quality but we gave it absolutely everything."
Morocco advance as runners-up. They came from behind twice to outwit Haiti 4-2 in Atlanta.
"We scored two goals, we are really proud of it," said Haiti striker Isidor after their third defeat at the 2026 tournament.
"The emotions were big. It is still really frustrating because we didn't get a point," he added.
"With the generation we have, I am confident we are going to be here again to win Haiti's first point in a World Cup."
