The Chiefs scored five tries to collect a bonus point that moved the New Zealanders to the top of the table after eight rounds.
Prop Arizona Taumalolo bagged two tries while wing Lelia Masaga and centres Sonny Bill Williams and Richard Kahui picked up one apiece in a match that was in the balance until the last three minutes.
Replacement flyhalf Johan Goosen claimed 16 points for the Cheetahs in only 30 minutes on the field with a try, a conversion and three penalties.
He is the tournament's leading scorer this season on 127 points.
Earlier, Cheetahs starting flyhalf Sias Ebersohn slotted four penalties and replacement flanker Ashley Johnson dived over for a try.
Taumalolo's first try in the 47th minute helped give the Chiefs a 17-9 advantage but their opponents quickly turned the game around to lead 22-17.
A second try by Taumalolo in the 57th minute put the Chiefs back in front before Goosen levelled matters at 25-25 with his second penalty.
Williams scored six minutes from time and Kahui crashed over three minutes later to seal the win.
Goosen then landed a 56-metre penalty on the final whistle to earn the South Africans a bonus point for losing by fewer than seven points.
