Son, who plays for Premier League club Totttenham Hotspur, provided the assist for the second goal before being substituted in the 72nd minute. He would be exempted from mandatory military service if South Korea win the competition.
All able-bodied South Korean men must complete 21 months service in the military as a deterrent against the North, but exemptions are offered to athletes who win gold at the Asian Games or a medal of any colour at the Olympics.
"We deserved to win, we had lots of chances to score," 26-year-old Son said after the victory. "I think we are better players so we dominated the game."
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The champions, who will play Japan or the United Arab Emirates in Saturday's final, grabbed an early lead when Lee scored the first of his two goals with a left-foot shot after Hwang Ui-jo tumbled trying to meet the through pass.
Hwang made amends just before the half-hour when Son fed him a through pass which he chipped over goalkeeper Bui Tien Dung.
Vietnam's occasional attacks mostly faltered before reaching the opposition box and South Korea keeper Jo Hyeon-woo was barely tested by a couple of tame long-range strikes.
Lee scored again 10 minutes into the second half when he latched onto a pass from Hwang Hee-chan.
Vietnam finally got on the scoresheet when Tran Minh Vuong buried a curling free-kick into the net in the 70th minute.
Son said neither he nor his team mates felt any pressure.
"We are so close to gold. We fight for that. I don't need to say anything, I am ready for that."
The defeat broke the hearts of hundreds of Vietnamese who thronged the Pakansari Stadium blowing vuvuzela, playing cymbals and waving flags.
South Korea advance to round of 16, Uruguay are out
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