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The Taeguk Warriors looked the favourite 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 – which began to play with real swagger – was 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.
