Hatim struck with just 12 minutes remaining to settle a scrappy game in which chances were rare.
The 2022 World Cup hosts Qatar will now face the UAE in the semi-final on Tuesday.
South Korean star Son Heung Min was largely kept quiet by the excellent Qatari defence, who have yet to concede in the tournament, though they had a let-off when Hwang Ui Jo's potential equalizer was disallowed for a marginal offside.
Qatar's midfielder Abdelaziz Hatim (C) celebrates his goal
The first semi-final is between record champions Japan and Iran on Monday with the final February 1.
In an attritional contest Hatim, who had earlier collected the booking which rules him out of the semi-final, produced a moment of quality to separate the teams.
His shot from 30 yards perhaps caught keeper Kim Seung Gyu unaware but hit the bottom corner at tremendous pace.
South Korea responded immediately when Hwang turned in Kim Young Gwon's cross but the assistant flagged and the video referee confirmed the decision was correct.
Omani fans cheering for Qatar
Captain Son and his side could not find another opportunity to level and it was Qatar's Boualem Khoukhi who went closer to the next goal with an acrobatic effort which was well saved.
South Korea will more regret Lee Chung Yong somehow missing at the back-post after keeper Saad al-Sheeb misjudged a cross and their inability to get the best out of Son, who often cut a forlorn figure out on the wing.
They were also unlucky when Kim Jin Su's free kick hit the post, with the game goalless, when Sheeb looked beaten.
A nondescript first half included only one shot on target, an effort from Qatar's Akram Afif easily held by Kim.
South Korea controlled possession but were one-dimensional and played in front of Qatar who rarely looked like losing their perfect defensive record before the break.
Son alternated on the flanks rather than his previous number 10 role but had little impact from either side.
Hatim, harshly, and Bassam Al Rawi, deservedly, picked up yellow cards that rule them out of the next game though Qatar can welcome back Abdelkarim Hassan and Assim Madibo who were banned from their first victorious quarter-final from three attempts.
