The Scots hauled themselves back into the match in Bloemfontein after trailing 14-0 at the interval, with scrum-half Sam Hidalgo-Clyne scoring all 13 points in nine second-half minutes - but the hosts raced away in the closing stages.
The Cheetahs opened the scoring in the 27th minute when full-back Craig Barry raced on to a chip ahead to touch down and Fred Zeilinga converted.
The hosts went over again in the first period through second row Rynier Bernardo, with Zeilinga adding the extras, and led 14-0 at half-time.
Edinburgh, who had won their previous four matches in all competitions, cut the deficit to 14-3 via a penalty from Hidalgo-Clyne, who then darted over for a try he converted before adding another three-pointer.
But number eight Junior Pokomela went over for the Cheetahs’ third converted try in the 59th minute and further touchdowns in the closing stages from left wing Makazole Mapimpi and replacement scrum-half Tian Meyer sealed a comfortable victory.
Cheetahs (14) 33
Tries: Barry, Bernabo, Pokomela, Mapimpi, Meyer. Cons: Zeilinga 4
Edinburgh (0) 13
Try: Hidalgo-Clyne. Con: Hidalgo-Clyne. Pens: Hidalgo-Clyne 2
Cheetahs: Blommetjies, Obi, Small-Smith, Lee, Mapimpi, Zeilinga, Venter, Marais, van Jaarsveld (C), Coetzee, Wegner, Reniel, Schoeman, Bernardo, Pokomela. Replacements: du Toit, Nche, Botha, Wiese, Maartens, Meyer, Kruger, Barry.
Edinburgh: Kinghorn, Fife, Johnstone, Dean, Van der Merwe; Tovey, Hidalgo-Clyne; Rizzo, Cochrane, McCallum, Bresler McKenzie (C), Carmichael, Crosbie, Mata. Replacements: Fenton, Sutherland, K Bryce, Hunter-Hill, Bradbury, Fowles, van der Walt, Rasolea.