The Cheetahs dominated first-half territory and possession but Johan Goosen missed three shots at goal and the Chiefs led 10-3 at the interval through Liam Messam's try.
The Chiefs stretched their lead early in the second period through Ben Afeaki before Asaeli Tikoirotuma, Gareth Anscombe, Rhys Marshall and Ben Tameifuna touched down against the tiring Cheetahs to secure a second bonus-point win from two matches.
Anscombe finished with 20 points, also kicking six conversions and a penalty.
"There's nothing like a good telling off at half-time," Messam said. "We got our backs some clean quick ball."
It was not all good news for the Chiefs, however, as they could be without Bundee Aki for next week's match against the Stormers in Cape Town after the centre limped off following a blow to his left thigh.
A six-try bonus-point win was a distant prospect for the Chiefs when they conceded three penalties in the first eight minutes and trailed 3-0 to a place kick from Goosen.
Cheetahs openside Pieter Labuschagne was especially prominent in the loose as the Bloemfontein-based side, beaten by the Sharks in their opener, dominated on all fronts.
But when the Chiefs finally got their hands on the ball, some sparkling back line play carried them up the other end and earned a penalty.
The home side opted for a lineout and worked the ball across to the other side, where Augustine Pulu was brought down just short of the line. Messam was picked up and shoved over from close range.
Afeaki stretched the lead following great work from Brodie Retallick, who charged down a clearing kick from Goosen and then raced to get to the loose ball ahead of the visiting defence.
The lock just managed to fingertip the ball toward the left touchline, where Afeaki scooped up and went over from a couple of yards.
Anscombe's conversion made it 17-3 and the Chiefs were firmly in control despite conceding 69 percent of territory up to that point.
Tikoirotuma scored off Aaron Cruden's composed pass behind his own back and the All Blacks scrum-half also created a half-gap for Anscombe to exploit and go over.
Marshall pumped his legs to propel two opponents back over the line and touch down before Tameifuna charged and rolled through two challenges to claim the final try in the closing minutes.