Sifiso Vilakazi, Sameegh Doutie, Mabhuti Khenyeza and Eduardo Ferreira scored for the Urban Warriors, who completely dominated the Dube Birds, for whom substitutes David Radebe and Mark Haskins found the net.
The visitors started the match at break-neck pace and deservedly went ahead in the seventh minute when Granwald Scott weaved his way into the area from the right flank before delivering a superb cross for Vilakazi to head home at the near post.
Craig Rosslee’s men doubled their advantage a minute later when Vilakazi dispossessed Swallows defender Davi Rancan on the left flank before crossing into the area for Doutie to fire home.
Swallows’ first real chance arrived in the 20th minute when Lefa Tsutsulupa unleashed a fierce shot from the edge of the area, but Ajax keeper Sean Roberts made a comfortable save.
Khenyeza made it 3-0 on the half hour mark when he headed home another good cross by Scott, as the visitors continued their dominance over Julio Cesar Leal’s men.
Roberts produced a superb save five minutes later when he denied Ryan Botha from hitting the back of the net with a good volley from the edge of the area.
Roberts was called into action again in the 39th minute when he denied Cecil Oerson’s header from hitting the back of the net and although the Swallows winger was able to gather the rebound, his effort from inside the six-yard area was cleared off the line by Martin Carelse.
Swallows striker Sandile Ndlovu should have pulled one back for the hosts seconds later when he found himself unmarked inside the Ajax area, and with just Roberts to beat, but the lanky striker’s powerful effort came crashing back off the crossbar.
The score remained 3-0 at the break.
Swallows gave a better showing in the second half, but again it was Ajax Cape Town who drew first blood when Ferreira made it 4-0 with a superb header from a corner by Doutie in the 67th minute.
Swallows then pushed more men forward and deservedly pulled one back via a header by substitute David Radebe from a good cross by Phumelele Bhengu in the 71st minute.
Fellow Swallows substitute Mark Haskins made it 4-2 five minutes from the end when he headed home a good cross by Morgan Shivambu.
However, it was all a little too late for the Dube Birds as the Urban Warriors tightened their defence to see out the final few minutes.