Ghana scored three goals in a World Cup match for the first time
A 10-minute spell in the first half by the African nation gave them a 2-0 lead courtesy of goals from Southampton defender Mohammed Salisu and Ajax's Mohammed Kudus.
However, noisy celebrations by Ghana fans at half time were dampened by a South Korea comeback after the break.
Two stunning headers in three minutes from Cho Gue-sung, the top scorer in his domestic league, levelled the game after 61 minutes.
But the impressive Kudus, who had deftly headed in Jordan Ayew's cross in the first half, added a final twist when he thumped in a third for Ghana to break South Korea's hearts.
Chances continued to fall South Korea's way as they searched for another equaliser but, despite 10 minutes of added time, Ghana held on.
There were emotional scenes at the final whistle as many South Korea players fell to the ground while manager Paulo Bento was sent off for arguing with English referee Anthony Taylor for not allowing a corner to be taken despite the 10 minutes having elapsed.
"We had the opportunity to have a corner kick, the referee took that opportunity away from us," assistant coach Sergio Costa said afterwards.
"Paulo [Bento] reacted, I was close by and he said nothing that was inappropriate to the referee. It was a reaction from a person that felt a lack of fairness at the end of the match.
"It is a normal reaction from someone that did everything to win and didn't. We can feel sad and we can feel a lack of justice. We gave our souls on the pitch."
In contrast, elated Ghana substitutes sprinted onto the pitch to celebrate as fans in the stand blew whistles and danced in celebration.
With Portugal to come next for South Korea, this feels a significant defeat, while Ghana - unfortunate to lose against Portugal - will face Uruguay knowing a win will take them through to the last 16 and a draw might be enough.
Portugal defeated Uruguay 2-0 in Monday's late match to confirm their progression to the knockout stage.
Ghana fans were in great voice throughout and celebrated loudly at the end
It was a frenetic game from beginning to end as both teams enjoyed spells of pressure without ever gaining sustained control.
South Korea started quickly, winning numerous corners and getting star forward Son Heung-min of Tottenham Hotspur on the ball regularly.
He was locked in a battle with young Brighton full-back Tariq Lamptey down the left wing but Ghana defended well and limited South Korea's chances.
Then came Ghana's two goals in 10 minutes and as Bento's side trudged off at half time, a way back into the game did not appear likely.
Southampton's Salisu pounced on a scramble in the box to poke in the opener after 24 minutes before Kudus flicked on Ayew's cross and sprinted to the corner flag in delirious celebration.
But Gue-sung suddenly had South Korea fans on their feet - with some even close to tears - as two superb headers brought the teams level and briefly silenced the dancing Ghana supporters.
The momentum was with South Korea but Kudus was clinical when he thumped in a third and decisive goal after team-mate Inaki Williams had missed a cross from the left.
Ghana goalkeeper Lawrence Ati Zigi made several saves in the closing minutes as South Korea poured forward but to no avail.
The scenes at full time indicated the importance of the result to both teams, the real significance of which will be felt after the Uruguay-Portugal game in Monday's late kick-off in Group H.
"The second half was totally different. We had control, possession and opportunities to score but the result at the end is totally unfair," added South Korea's Costa.
"Not even a tie would have been fair. We clearly deserved to win. I think we can be very proud of what we did and can count on us in the next match."
-- Courtesy of BBC Sport