Second-half goals from Kim Jin-su and Kwon Chang-hoon on Tuesday gave the Koreans a comfortable victory over the bottom team in Asia Group A qualifying.
Iran is on top of Group A with 16 points from six games with South Korea two points behind in the second of the two automatic qualification spots, eight ahead of United Arab Emirates (UAE) in third.
Australia edged Vietnam 1-0 in Hanoi while Japan defeated China by a solitary goal in Doha; Kwon Chang-hoon's 2nd half goal sealed the win for South Korea against Lebanon.
Yoo played 124 times for South Korea from 1994 to 2005 and was a leading member of the team that reached semi-finals of the 2002 World Cup.
Since FIFA has operated the World Cup with 32 teams, only Chile has advanced to the round of 16 after earning three points in the group stage.
Mexico, which upset defending champion Germany in their opening match, took the lead when Vela converted from the penalty spot in the 26th minute.
Sweden captain Andreas Granqvist converted from the spot, sliding his shot into the bottom right corner in the 65th minute.
South Korea have two draws and two losses from their four previous encounters with Sweden, although their last meeting was in 2005.
Germany, Mexico, Sweden and South Korea are part of Group F of the FIFA World Cup 2018.
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