Qatar now stands five points behind third-place Uzbekistan and will need to win both their final games in Group A -- and hope Uzbekistan lose both -- to stand a chance of qualifying, reports Xinhua news agency.
Meanwhile, South Korea remain a point ahead of Uzbekistan in the race for the automatic second qualifying spot in the group.
The team that finishes third will enter a playoff over two legs for a place in the 2018 World Cup.
Qatar largely owed its victory to the shining performance of Hassan Al-Haydos and young forward Akram Afif.
Al Haydos put Qatar on the board in the 25th minute on a free kick, set up after a South Korean turnover. Afif scored Qatar's second goal in the 51st minute, but the home side's fragile defence could not stand firm.
Goals from South Korea's Ki Sung-Yueng and Hwang Hee-Chan in the 62nd and 69th minute seemed to have secured South Korea a valuable point in their attempt to get to Russia, but fine work from Brazilian-born Rodrigo Tabata set up Al-Haydos for a 74th-minute winner.