South Korea had all the early pressure, forcing seven corners in the first 20 minutes, but it was Mohammed Salisu who gave Ghana the lead against the run of play after a goalmouth scramble (24).
Kudus doubled the advantage (34) with a precision glancing header after a beautifully delivered Jordan Ayew cross from the left-hand side.
Cho Gue Song scored two quick-fire headers to bring South Korea back on level terms around the hour-mark, before Kudus added his second of the game in the 68th minute with a well-taken finish to make it 3-2.
Salisu was forced to clear off the line late on to ensure Ghana came away from the Education City Stadium with all three points, keeping their hopes of qualifying for the knockout stages well and truly alive.
Ghana’s first win of the tournament means they are in control of their own destiny in terms of qualifying for the knockout stages heading into their last match against Uruguay on Friday.
South Korea can still qualify for the knockout stages but they will need to beat Portugal in their last group game on Friday.