South Korea, who have appeared at every World Cup since 1986, went ahead through Oh Se-hun four minutes before half-time but Aymen Hussein's overhead kick five minutes into the second half levelled the score.
Oh Hyeon-gyu restored Korea's lead with 16 minutes remaining and Lee Jae-sung scored his side's third nine minutes later to leave Ibrahim Bayesh's 95th minute goal as nothing more than a consolation.
Jordan jumped ahead of the Iraqis and into second place on goal-difference in the group with a 4-0 trouncing of Oman as Yazan Al Naimat and Ali Olwan each scored twice in Amman while Palestine picked up a point with a 2-2 draw against Kuwait.
Uzbekistan needed a 76th-minute penalty from Otobek Shukurov to beat 10-man United Arab Emirates 1-0 in Tashkent and Iran kept pace with a 4-1 come-from-behind thrashing of Qatar. The pair are now six points clear.
Almoez Ali put Asian Cup holders Qatar in front with a first-time strike in the 17th minute but Sardar Azmoun scored either side of the interval to put Iran ahead.
Mohammed Mohebi added the third in the 65th minute and put the seal on the win deep into injury time.Â
Kyrgzstan beat North Korea 1-0 in the group's other match.
In Australia's Group C China picked up their first win as Branko Ivankovic's side defeated Indonesia 2-1 in Qingdao with first-half goals from Behram Abduweli and Zhang Yuning securing the three points. The pair remain the bottom two in the six-team section.
The top two finishers in each of Asia's three qualifying groups advance to the World Cup while the third and fourth-placed nations progress to a further round of preliminaries.
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