Both locks Manual Carizza and Eben Etzebeth had to leave proceedings in the first half, with the biggest concern expressed over Carizza’s departure.
Etzebeth was probably just substituted after leaving the field just before halftime, but Carizza took a big knock after just 15 minutes.
The Stormers scored five tries to four, but after leading 29-10 at the break and 39-17 deep in the second half they were never in danger of being caught, although the Cheetahs ran in the last two tries by flank Tienie Burger and wing Cornal Hendricks who completed his brace of tries.
Earlier flank Jean Cooke and Hendricks scored the Cheetahs first two tries to reduce the Capetonians lead to 29-17 shortly after the break.
Flyhalf Willie du Plessis converted two and also added a penalty, while replacement pivot Francois Brummer also weighed in with two conversions.
In the first half Stormers tries by centres Juan de Jongh and Huw Jones, hooker Scarra Ntubeni and scrumhalf Nic Groom ensured the Stormers dominated the opening period.
In the second half however they could add only one more try by wing Dillan Leyds with flyhalves Demetri Catrakilis (four conversions) and Kurt Coleman (two penalties) adding the rest with their boots.