The Koreans had been held to a dismal 0-0 draw with Syria in their last Group A encounter and were determined to get a quick goal to settle their nerves against Qatar in Suwon.
Skipper Ki Sung-yueng duly obliged with a rifled 11th minute opener but the hosts' frailties at the back was exposed by Andres Quintana, who earned a converted penalty before scoring Qatar's second to put the visitors 2-1 ahead.
The Koreans, aiming for a ninth consecutive appearance at the World Cup finals, equalised through Ji Dong-won before Son Heung-min grabbed the winner in the 58th minute and the 10-man hosts held on in the closing minutes.
With a difficult trip to Iran up next on Tuesday for the Koreans, tightening up at the back must be a priority for Stielike but the German said he would not temper his side's attacking style.
"We focus on attack and this means we can be vulnerable against counter attacks," he was quoted as saying by Yonhap news agency on Friday.
"However, we're not going to change our style of play and philosophy, although we do need to carefully boost our defence."
South Korea trail leaders Iran on goal difference with seven points from three games, with Uzbekistan a point behind.
The top two in Group A and B qualify directly for the 2018 World Cup while the third-placed teams meet to decide who goes into a CONCACAF-Asian Zone playoff for another place at the finals.
The Koreans will be without defender Hong Jeong-ho in Tehran after he was dismissed in the 66th minute following the second of two fouls on Quintana, though Stielike may have been tempted to drop him regardless for his poor performance on Thursday.
"I know there are still big concerns and criticism against our team," said Stielike. "I'm a little bit concerned about our future performance in a situation where we're not getting big support from fans despite collecting a victory with 10 men."
(Reporting by Peter Rutherford; Editing by John O'Brien)
