The substitute toe-poked from just a yard out deep into stoppage time after a speculative effort came off the crossbar, sparking delirium in the Seoul World Cup Stadium as the South Koreans provisionally topped Asia's Group A.
The hosts had earlier blown a 1-0 second-half lead and were drawn into some unsavoury exchanges, including a mass pushing and shoving match with five minutes to go, as a disappointing draw beckoned.
But Son's strike was golden as it gave the 2002 FIFA World Cup semi-finalists a third win from five games in the final qualifying round to leave them two points clear with three to play. The South Koreans struggled to capitalise on their huge advantage in possession for most of the match, while the visitors were apparently willing to sit back and walk away with a draw.
The hosts had little to show for their efforts around the Qatari area. In the 25th, Ji Dongwon took a nifty pass from Augsburg team-mate Koo Jacheol but miscued his shot from the left edge of the box. About eight minutes later, Lee Chungyong fed striker Kim Shinwook deep in the area, but goalkeeper Qasem Burhan was quicker to the ball.
In the 36th, Lee Keunho crossed for Lee Chungyong but the Bolton Wanderers midfielder fluffed his chance. Shortly afterwards, Kim Shinwook's shot deflected off Qatari defender Ibrahim Majed.
It was much the same story in the second half. Lee Chungyong received a header from Ji Dongwon in the 50th minute but his rolling shot from the top of the 'D' rolled just wide of the right post. Substitute Lee Donggook headed a Ki Sungyueng free kick in the 55th minute but it went right at Burhan in goal.
Lee Keunho finally put the home team on board in the 59th by superbly glancing Park Wonjae's cross into the Qatari goal. But Qatar drew level just three minutes later as Khalfan Ibrahim buried a low shot past Korean 'keeper Jung Sungryong.
The game grew testy in the closing stages, with Son sparking a late melee when he appeared to kick out at Hamed Ismaeil following a heavy challenge.
But despite the fraying tempers, Son kept his wits about him and he was on hand to nudge the late, late winner over the line.