But they had to withstand a spirited finish from their opponents to claim a 10th win of the season as the Cheetahs scored two late tries.
The win keeps the Bulls second in the overall standings, two points behind the defending champions Chiefs from New Zealand. Australia's Brumbies also have 54 points but the Bulls edge them on points differential.
Hopes for a high-scoring showdown at the Free State Rugby stadium were lifted early on when Bulls prop Werner Kruger went over in the corner for the game's first try after 10 minutes.
But the Cheetahs, who had lost 11 successive matches to the Bulls, struck back when winger Willie le Roux produced a piece of individual brilliance, chipping over the defence at pace and running through to collect the perfect bounce and dive between the posts.
The visitors' dominance at the lineout was rewarded soon after, however, when flanker Deon Stegmann scored his side's second try on 19 minutes as they drove over the Cheetahs' goal line from close range.
The Bulls' seven-point halftime lead was extended when substitute scrum half Jano Vermaak broke through with less than a quarter of an hour to play.
The Cheetahs hit back - fly-half Riaan Smit going over in the corner and television replays confirming replacement prop Trevor Nyakane had grounded the ball - but despite the home crowd of 32,000 willing them on, they couldn't complete their comeback.