The defensive midfielder's left-footed shot came out of the blue in the 78th minute and flew past RoK goalkeeper Kim Seung-gyu to decide a largely disappointing contest in front of a crowd of only 13,700 at Zayed Sport City.
Twice former champions RoK poured forward to try and rescue the match but were unable to produce an equaliser.
The political rift between Qatar and the UAE meant the Maroons were supported by only a couple of hundred Omanis but they celebrated wildly in front of them at the final whistle.
Pre-tournament favourites RoK, who had been looking to reach the last four for a record-extending 11th time, bowed out before the semi-finals for the first time since 2004.
Both teams had played their last 16 matches on Tuesday, which perhaps contributed to a forgettable first half with just one shot on target -- Akram Afif's long-range effort after 32 minutes which RoK keeper Kim safely gathered.
The Qataris, who started with five at the back, came out with more attacking intent in the second half but were almost immediately caught on the break with Hwang Ui-jo forcing a save out of Saad Al Sheeb.
The game was opening up with chances at both ends and Son, who had looked fatigued since joining the RoK squad for their third group game, started to impose his influence.
The Tottenham Hotspur forward got a low drive on target in the 72nd minute which went straight to Saad and made a decoy run before Kim Jin-su curled the ball onto the outside of the post from a free kick three minutes later.
Just when it looked like the Koreans might be getting on top, though, the ball broke for Hatem in midfield and seconds later it was nestled in the bottom right-hand corner of the RoK net.
Hwang Ui-jo had the ball in the back of the opposite net two minutes later but was ruled offside, a decision confirmed by the video assistant referee, and Qatar held on to secure a famous victory.
Australia’s defence of their AFC Asian Cup title came to an end on Friday evening as Ali Mabkhout’s second half goal earned tournament hosts the United Arab Emirates a 1-0 win over the Socceroos and set up a semi-final meeting with Qatar.
Mabkhout took advantage of an under-hit back pass midway through the second half to steal in behind the Australian defence and round Maty Ryan to register the only strike of the game.
Alberto Zaccheroni’s side will now take on Qatar with a place in the final at stake as the hosts moved one step closer to emulating their run to the deciding game when the tournament was last held in the UAE in 1996.
