South Korea drew 1-1 with second-placed Jordan in Suwon after registering the same scoreline against Oman in Goyang last week.
Two wins would have seen South Korea automatically qualify for the tournament with two matches to spare.
Now they face a tricky away trip to Iraq in June and a final home clash against Kuwait in their final two fixtures needing four points to be certain of progressing without having to rely on other results.
Jordan are three points behind South Korea but Iraq can leapfrog them and close the gap to one point at the top of Group B if they beat Palestine in Amman later.
Lee Jae-sung put the hosts ahead in the fifth minute when he turned in Son's corner unmarked from close range.
But that was as good as it got for the Koreans, who had the lion's share of possession but lacked penetration in attack.
Jordan carried a threat on the break and equalised through Mahmoud Al Mardi's deflected shot in the 30th minute.