Defender Thapelo Tshilo netted in the 27th minute with an emphatic finish in the box after Dikwena failed to deal with a corner from Jabulani Maluleke.
Zimbabwean attacker Walter Musona had a chance to double the lead in the 40th minute, but his attempt was well saved by Mbongeni Mzimela.
The visitors, who lost the reverse fixture 3-2 in Rustenburg, threatened in the second period via efforts from Sibusiso Msomi and Willem Mwedihanga, but goalkeeper George Chigova was equal to the task.
The win saw City rise to sixth place on the table with 31 points from 24 matches, while Stars remain 11th with 25 points from 23 games - four points above the drop zone.
