The Bulls scored six tries, two of them after scrumhalf Francois Hougaard was sent off for a tip tackle, and flyhalf Morne Steyn became the third player and first South African to reach 1000 points in Super rugby.
Steyn converted every try and added three penalties, missing just one shot at the posts from 10 attempts. The miss was from halfway.
The Cheetahs were game but outgunned by a side starting a dozen Springboks in the second round. They conceded the bonus-point fourth try to the Bulls right on halftime and scored their only try when they were playing 14 men.
The Bulls made the Television Match Official work early. He disallowed a try to left wing Bjorn Basson, who was bundled into touch by Robert Ebersohn, but two minutes later he agreed that prop Dean Greyling scored with three Cheetahs on his back.
Fellow prop Werner Kruger was driven over and Basson was on the end of a backline chain for the third try.
Steyn's conversion of Basson's try brought up a personal 1000 points in Super rugby. His 21-point match haul lifted him to 1012, behind only the Crusaders' Dan Carter (1272) and ACT and Melbourne star Stirling Mortlock (1031).
Counterpart Johan Goosen kicked his fourth penalty to leave the Cheetahs 24-12 behind, but as the halftime hooter sounded, Bulls centre Wynand Olivier made a clean break, Akona Ndungane backed him up, and fullback Zane Kirchner was inside for the final pass.
The Cheetahs' best period of attack was the first 10 minutes of the new half, but every charge was stopped by a Bull.
Frustrated, the Cheetahs conceded two penalty kicks to Steyn, then Hougaard was red-carded in the 63rd for a tip tackle on Ebersohn.
The Cheetahs ran the penalty and captain Adriaan Strauss scored the converted try.
But the Bulls always had a reply. JJ Engelbrecht, just on as a replacement, intercepted Cheetahs midfielder Philip Snyman for an easy run-in, then Kirchner produced a neat solo try when he regathered a chip kick over the defense and finished between the posts.
The Bulls played out the last three minutes with 13 men when flanker Jacques Potgieter was sin-binned for a shoulder charge on Heinrich Brussouw.
Bulls 51 (Zane Kirchner 2, Dean Greyling, Werner Kruger, Bjorn Basson, JJ Engelbrecht tries; Morne Steyn 6 conversions, 3 penalties), Cheetahs 19 (Adriaan Strauss try; Johan Goosen conversion, 4 penalties). HT: 31-12
