Centre Ronnie Cooke opened the scoring when he pounced on a Cheetahs midfield error to kick the ball through, gather and dive over.
The Cheetahs hit back from a penalty five metres from the Kings line when skipper Adriaan Strauss bashed his way through to level the scores.
But the Kings showed a willingness to send the ball wide to give fullback Shakes Soyizwapi two tries.
The second was a remarkable effort and came with the Cheetahs on the attack and the ball ending up behind the Kings' line, only for wing Michael Killian to claim possession and to start an attack down the left flank.
The movement ended with Soyizwapi crossing for a thrilling try in the right corner after the ball had gone the length of the field.
Jean Cook scored his first try two minutes before half-time and then the Cheetahs took control in the second half, denying the Kings the possession they needed to launch an attack.
The Cheetahs forwards dominated most phases and it was only the spirited fighting qualities of the Kings which kept them from running away with the game.
Eventually, though, the pressure told and Prinsloo crossed for his second try two minutes before the final whistle to secure a solid win for the visitors.
SCORERS
Cheetahs 36: Tries by Jean Cook (2), Boom Prinsloo (2), Adriaan Strauss, Raymond Rhule; conversions by Elgar Watts (2), Johan Goosen (1).
Southern Kings 21: Tries by Shakes Soyizwapi (2), Ronnie Cooke; conversions by George Whitehead (3).
- Sapa