The Black Stars, despite being under the cosh for most of the first half, went two goals to the good through Mohammed Salisu and Mohammed Kudus before the break.
However, South Korea came back with a bang through a pair of Cho Gue-sung headers, but Kudus's second of the match settled an enthralling affair, after which South Korea head coach Paulo Bento was sent off at the full-time whistle for lambasting referee Anthony Taylor over a corner which they had no time to take.
After failing to make a succession of corners count in the early exchanges - seven in 17 minutes to be exact, with the final one seeing Son Heung-min try and fail to connect with a bicycle kick not long after - South Korea were made to pay the price, ironically from a set-piece.
Ghana were awarded a free kick on the left-hand side in the 24th minute, and Jordan Ayew sent in an inviting inswinging ball, which South Korea failed to deal with, and Salisu was the quickest to smash home the loose ball.
Replays showed that the ball had come off Andre Ayew's hand on its way down to the Southampton defender, but the goal was awarded despite a VAR check, as Otto Addo's side took the lead completely against the run of play.
After South Korea failed to deal with one inswinging cross from the left by Jordan Ayew, a carbon copy of the Crystal Palace man's stunning ball into the box led to a second for Ghana in the 34th minute, as Kudus ghosted in to meet his compatriot's inch-perfect delivery and guide a deft header home.
For all of their shots on goal and dominant spells of possession, South Korea found themselves two goals down at the break, but they finally posted their first shot on target of the 2022 World Cup early in the second half.
Cho directed a powerful header towards goal in the 53rd minute, but Lawrence Ati-Zigi made a save for the cameras, diving high to his right to palm the ball away.
However, Bento's men would make a near-identical delivery count in the 58th minute, as Lee Kang-in crossed from the left for Cho to have a second bite at the cherry, and the 24-year-old's low header flashed past Ati-Zigi into the back of the net.
Only three minutes later, South Korea were suddenly level via another Cho header, as Kim Jin-su did well to keep the ball in play and cross from the edge of the byline, and his compatriot leapt highest to erase Ghana's two-goal lead.
The South Korea contingent in the crowd were elated, but that soon turned to despair, as in the 68th minute, Inaki Williams failed to properly connect with Gideon Mensah's low cross from the left, but the ball found its way to Kudus, who side-footed in his second of the match.
A goal-laden contest showed no signs of slowing down in the latter exchanges, as Salisu cleared an effort from Kim Jin-su off the line in the 76th minute, just after Ati-Zigi got down low to keep out Lee Kang-in's goalbound free kick.
No fewer than 10 minutes were added on at the end of the second half, during which South Korea were unsurprisingly doing most of the attacking in their desperate search for another equalizer.
A late shot from Lee Kang-in sailed over the bar before Taylor blew his whistle after the ball went out for a South Korea corner, infuriating Bento and leading to a red card for the Portuguese-born coach for his protests.
Ghana now sit second in Group H with three points ahead of their final group game with Uruguay on Friday, while South Korea are bottom with one point before their showdown with Portugal in four days' time.