Goals from Lee Jae-sung and Oh Hyeong-gu gave under-fire coach Hong Myung-bo his second win in a row and lifted the Koreans on to seven points from three matches.
Hong had been booed after Korea's opening 0-0 draw with Palestine in Seoul but back-to-back wins mean the Taeguk Warriors are in a strong position to continue their record of qualifying for every World Cup since 1986.
A header from Lee gave South Korea, missing injured captain Son Heung-min, the lead in the 38th minute and Oh doubled the advantage 23 minutes into the second half when he wrong-footed Yazeed Abulaila to score from inside the area.
In group A, Uzbekistan were unable to find a way past Iran's defence despite the visitors having only 10 players for the final 35 minutes of their top-of-the-table clash as they played out a 0-0 draw in Tashkent.
Defender Saleh Hardani was shown a red card 10 minutes into the second half for a dangerous tackle on Uzbekistan captain Eldor Shomurodov.
Australia picked up their first win of the campaign at the third attempt as Tony Popovic led them to a 3-1 victory over China in Adelaide in his first game since replacing Graham Arnold as coach.
The win revived Australia's chances of finishing the third phase of qualifying with a top-two spot and an automatic ticket to the 2026 finals.
China, who have conceded 12 goals in their three qualifiers, remained winless in group C.
The top two in each group advance automatically to the World Cup while the third and fourth-placed sides go into another round of preliminaries.
Group C leaders Japan were taking on Saudi Arabia in Jeddah later on Thursday while Bahrain were hosting Indonesia.
12°C