Goals from Lee Jae-sung and Oh Hyeong-gu gave underfire 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.
Oman eased to a 4-0 win over Kuwait in Muscat to move off the bottom of Group B with Abdulrahman Al Mushaifri scoring twice for Rashid Jabar's side.
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.
Asian champions Qatar won their first game of the third round with a 3-1 victory over Kyrgyzstan, Almoez Ali putting Tintin Marquez's side in front before Tamirlan Kozubaev's own goal doubled the home team's advantage.
Alimardon Shukurov pulled one back for the Central Asians but Ibrahim Al Hassan put the result beyond doubt with nine minutes remaining to move the Qataris up to fourth, level on four points with the United Arab Emirates.
United Arab Emirates drew with North Korea as Jong Il Gwan struck four minutes from time to earn his side a 1-1 draw in Al Ain.
Yahya Al Ghassani had put the home side in front and Han Kwang-song's 74th-minute penalty was saved by Khalied Eisa before Jong's late leveller.
Australia picked up their first win of the campaign at the third attempt as Popovic led them to a 3-1 victory over China in Adelaide in his first game since replacing Graham Arnold as coach.
Hometown favourite Craig Goodwin powered home a long-range strike in the 53rd minute after setting up Australia's first goal just before halftime with a free kick that was headed in by Lewis Miller to cancel out Xie Wenneng's opener.
Nishan Velupillay made sure of the win on his international debut with a stoppage-time goal.
Indonesia, meanwhile, were denied victory by hosts Bahrain deep into stoppage time when Mohamed Marhoon scored his second of the game to earn his side a 2-2 draw with the Southeast Asians, who have now drawn their last three matches.
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 take on Saudi Arabia in Jeddah later on Thursday while Iraq play Palestine in Group B.