After being held to a surprise 0-0 draw with Syria in their last Group A game, the Koreans were determined to get on the board quickly and got off to a great start when Ki Sung-yueng fired home from outside the box with 11 minutes gone.
That lead lasted just five minutes however, as Korean defender Hong Jeong-ho impeded Andres Quintana in the box and Hasan Al Haydos equalised from the penalty spot.
Qatar stunned the home crowd for a second time by taking the lead on the stroke of halftime.
The impressive Quintana harried Hong out of possession on the right and after his first attempt at goal was blocked Qatar worked the ball back to him and he flicked it confidently over Korean goalkeeper Kim Seung-gyu.
Korea coach Uli Stielike brought on Kim Shin-wook for the second half and the towering hitman made an instant impact, standing his ground well to nod Hong Chul's cross back across goal and Ji Dong-won swooped to make it 2-2 in the 56th minute.
Two minutes later, Korean skipper Ki released Son into the box with a clever pass and the Tottenham Hotspur forward curled home into the far corner of the net.
Son's goal settled Korean nerves, but not for long.
Hong, who had been booked for hauling down Quintana for the penalty, then picked up a second yellow card in the 66th minute for fouling the same player.
Qatar pressed hard for the equaliser and Quintana spurned their best chance late on when he bulleted a header straight at Kim from close range.
Son, who has scored five goals in six games for Tottenham Hotspur this season, paid tribute to his captain for steadying their nerves when Korea fell behind.
"The players were very surprised but Ki held us together,” he told local media.
Coach Stielike said he never lost belief despite falling behind.
"Even when we were 2-1 down I kept encouraging the players that we could do it," he said. "This is the first comeback win since I took over. It will give the players confidence before we head to Iran."
Korea, top of the group on seven points from three games, travel to Tehran for their next fixture on Oct. 11. Iran are playing Uzbekistan later on Thursday. In the day's other group game, Syria stunned hosts China 1-0.
(Writing by Peter Rutherford, editing by Pritha Sarkar)
