The win solidifies Ajax’s position at the top of the table, three points clear from Bloemfontein Celtic, while Swallows drop down to sixth.
First half goals from Mfundo Shumana and Russel Mwafulirwa put the Urban Warriors in the driving seat before they faced a nervy final 15 minutes when Sandile Ndlovu brought Swallows back into it.
However, late strikes from substitute Nhlanhla Shabalala and Terror Fanteni made the margin of victory more flattering for the home side.
But the evening started badly for Ajax when they lost leftwing Franklin Cale through injury after just 11 minutes, to be replaced by Jonathan Fransman.
They were ahead after 23 minutes however, when Fanteni’s excellent cushioned ball from the cross teed-up Shumana, who rifled the ball into the top corner of Aubrey Mathibe’s goal from ten yards.
Swallows tried to hit back as James Chamanga found space in the penalty area, but his shot was blocked, and just a minute later Bryce Moon was incorrectly given offside at the other end of the pitch when one-on-one with the goalkeeper.
But five minutes later Ajax did have their second goal and once again Fanteni was the provider. His defence-splitting pass put Mwafulirwa through and although his shot was half stopped by Mathibe, it had enough on it to cross the goalline.
The Birds’ coach Ian Gorowa had seen enough and made a double substitution on 41 minutes, with Hellings Mwakasungula replacing Mark Haskins and Tsweu Mokoro entering the fray for the ineffective Songwe Chalwe, but the score remained 2-0 at the break.
The first 30 minutes of the second half was a frustratingly stop-start affair, but Swallows gave themselves a lifeline on 75 minutes when Mokoro’s cross to the far post found the head of Ndlovu and he headed across Hans Vonk and into the goal.
Mwakasungula then warmed the palms of Vonk from 25-yards with seven minutes remaining as Swallows pushed forward for an equaliser, dominating possession in the closing stages.
But the points were sealed a minute from time as Nathan Paulse beat the offside trap and fired a shot at Mathibe from an angle, the ball rebounding to Shabalala, who had the easiest of tap-ins into an empty net.
And there was still time for one more when Fanteni stole in at the neat post to beat Mathibe following a low ball in from the right.