Goals from Katlego Mphela, George Lebese and Bernard Parker sealed an impressive rout for Chiefs and put them back in the driving seat for the Premiership title.
Chiefs played with energy and dominated the game from start to finish, never looking in trouble of dropping points.
Even when Swallows tried to push forward in the early stages, Amakhosi's defence was able to snuff out the danger before any real problems could be caused.
Mphela popped up and duly headed Amakhosi into the lead.
Despite their dominance throughout, Chiefs fans had to wait until the 85th minute before they could finally breathe easy.
Parker was again involved by providing the pass to goalscorer Lebese, who noticed Etafia coming off his line and deftly chipped the Nigerian keeper.
The Soweto club put the game beyond a shadow of a doubt two minutes later when undoubted Parker won the ball in the Swallows box before calmly slotting home for a deserved goal.
Amakhosi went in to the game desperately in search of a positive result after only managing one Premiership win in 2015.
The Soweto giants were determined to get their season back on track after a dismal showing in the CAF Champions League in midweek when the lost 1-0 to Raja Casablanca at home, and it showed.