Attacking trio Edward Manqele, Siyabonga Nomvethe and Lerato Chabangu got the goals for Swallows, with Keagan Dolly on target for the Urban Warriors at Cape Town Stadium.
The result leaves the Dube Birds with 18 points from 10 games - eight points ahead of 12th-placed Ajax.
On eight minutes the visitors went ahead through a superbly-taken goal from Manqele. Chabangu was the architect, playing a perfectly weighted through-ball for the former Free State Stars striker, who beat goalkeeper Brandon Petersen with a low shot into the bottom corner.
The Cape Town side gradually began to get a foothold in the game and by the midway point of the first half they were beginning to create half-chances with regularity, though Greg Etafia’s willingness to come quickly off his line helped out his defence greatly.
The Nigerian goalkeeper made a brave, smothering block at the feet of youngster Tasriq Morris on 39 minutes and took a boot to the face for his troubles, though thankfully it was nothing serious.
It took just six minutes of the second half for the Birds to double their advantage. Winger Dikgang Mabalane sprinted free down the right and picked out Nomvethe with a cut-back – the veteran striker coolly picked out the bottom corner with his right foot to make it 2-0.
By the 62nd minute Urban Warriors coach Muhsin Ertugral had used all three of his substitutions in an attempt to spark his team into life, and within 10 minutes they pulled a goal back.
Lebogang Manyama played in Eleazar Rodgers, who saw his low shot well saved by Etafia, but youngster Dolly was able to steer the rebound into an empty net to put Ajax back in contention.