The Taeguk Warriors looked the favourites to go on and edge what was a thriller at Education City Stadium after fighting back from 2-0 down, but Kudus' second goal of the game proved decisive.
After a shaky start, Mohammed Salisu had the Black Stars ahead against the run of play, and Ghana – who then began to play with real swagger – were soon 2-0 up thanks to Kudus.
Cho Gue-sung scored with two brilliant headers in a ferocious three-minute spell for South Korea, but that brace did not prove to be the catalyst for victory, as Kudus' cool 68th-minute finish sealed it in Ghana's favour.
All the early purpose came from South Korea, with Daniel Amartey's vital intervention denying Cho a tap-in after just five minutes.
But Ghana weathered the storm and edged in front before the half-hour mark, Salisu smashing in from close range after Jordan Ayew's free-kick delivery caused havoc.
Another brilliant Ayew cross from the left brought a second goal 10 minutes later, as Kudus' glancing header found the bottom-right corner.
South Korea had hope just before the hour. Lee Kang-in robbed Tariq Lamptey and saw his exquisite cross guided home by Cho.
And the striker towered above the Ghana defence to equalise a few moments later.
But Ghana had the last laugh, as Kudus clinically found the bottom-left corner after Inaki Williams completely missed his kick, and South Korea never found a response, with head coach Paulo Bento shown a red card after the final whistle for arguing with the officials.
What does it mean? Uruguay revenge on the agenda for Black Stars as South Korea face up to big challenge
Regardless of what happens in the later game between Portugal and Uruguay, South Korea will need to beat the Selecao on matchday three, and they will probably need to do so by a few goals.
Essentially, qualification for the last 16 now looks highly unlikely, whereas Ghana have the bit between their teeth and will only need a point next time out.
This performance showed teams will always cause the Black Stars problems defensively, but they have talent going forward, and the opportunity for payback after Luis Suarez's infamous handball against them in 2010 will provide real motivation.
Kudos to Ghana
He was lively against Portugal; he was the star of the show here. Kudus is looking like one of the breakout stars of the tournament.
He may not have created any chances, but twice he was in the right place at the right time as he became the second youngest (22 years 118 days old) African player to score two goals in a World Cup match, after Ahmed Musa (21y 254d) for Nigeria against Argentina in 2014.
Salisu plays his part
His goal set Ghana on their eventual path to victory, though the centre-backs exploits at the back were just as key. As South Korea piled the pressure on at the end, he took his clearances tally to a match-high seven.
Kudus' positioning was key in attack; Salisu's was vital at the back.
Key Opta facts
- Ghana scored three goals in a single World Cup game for the first time in their history, while they have scored in each of their last seven World Cup matches overall – only Nigeria (8 between 1994 and 1998) have scored in more consecutive games among African nations in the competition.
- Ghana became the first team to record consecutive 3-2 results at the World Cup (for or against) since Uruguay in 2010 and the fourth side overall to do so (also Germany in 1994 and Switzerland in 1934).
- South Korea have won just one of their last 11 matches at the World Cup (D3 L7) and conceded as many goals here as they did in their previous four games in the competition.
- Ghana scored with all three of their shots on target in this match, having previously scored with two of their three shots on target against Portugal on matchday one at this World Cup.
- Cho became the first South Korea player to score more than once in a World Cup game, while he was the first Asian player to score two headers in a World Cup game.