Tuesday's loss leaves Korea second in their qualifying group, a point clear of third-placed Uzbekistan.
South Korea last failed to qualify for a World Cup in 1982, but they have not won away from home in over a year and struggled in the opening hour against their bottom-of-the-table hosts.
Later, the Qatari coach defended his players and stated, "I don't see something that can receive a punishment as it is a t-shirt with a picture of the Emir", he said.
Japan missed the chance to take a three-point cushion at the top of Group B, ahead of its final games against Saudi Arabia and Australia which are both just one point back.
It means Qatar, the 2022 World Cup hosts who have endured a terrible final round in the AFC qualifying competition, still have a remote chance of playing in Russian Federation.
As well as the action on the pitch, there was also plenty of drama off the pitch.
Even after Tuesday's impressive victory, secured by Hasan Al Haydos's victor 16 minutes from time, Qatar need to make up three points on third-placed Uzbekistan in Group A with only two matches remaining.
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She said she is now a grandmother and wants to end the media intrusion that she believes exists because the case is not settled. He was unable to up his 2002 best director Oscar for The Pianist because he feared arrest if he returned to the US.
Federation Internationale de Football Association bans any unsanctioned political, religious or commercial messages on shirts.
Korea got off to a slow start by allowing the lead to Qatar in the 25th minute.
After scoring, Haydos sprinted to the touchline and held up a t-shirt to the crowd.
Hwang Hee-chan restored parity and appeared to set the Koreans up for a dramatic win, until Al Haydos struck again to clinch the points.
Goals from Ki Sung-yeung and Hwang Hee-chan brought South Korea level with 20 minutes remaining, but Al Haydos scored Qatar's victor in the 75th.
"I fully understand we've not been playing well of late and I think I have to take the fall for that", Stielike was quoted as saying by Yonhap News Agency after the team returned from Doha.
Tottenham's Son Heung-Min went off injured in the 33rd minute after suffering a suspected broken right arm.