A youthful Amakhosi side, inspired by a brace from winger Mandla Masango, had too much pace and energy for the Birds and move to within two points of log leaders Mamelodi Sundowns, who are in action on Sunday afternoon.
The Birds will be disappointed at having suffered such a loss, but they only had themselves to blame after dominating large portions of the match but failing to capitalise on the chances they created.
Swallows were the better team in the opening quarter, though they only created one half-chance for Joseph Makhanya, whose angled drive from just outside the penalty area was comfortably saved by Itumeleng Khune.
On 25 minutes, somewhat against the run of play, Chiefs took the lead. George Lebese played in a good low cross from the left to pick out the unmarked Masango, whose scuffed shot trickled past the right hand of Greg Etafia and rolled over the goal-line.
Swallows almost replied on the half-hour mark when Lefa Tsutsulupa brought down a lofted cross with a brilliant first touch and got a quick shot away, but the ball flashed over the crossbar. Seven minutes later Makhanya crashed a long-range effort off the crossbar with Khune completely beaten.
It seemed as if the Birds would draw level before half-time such was the pressure they were creating, but Amakhosi made it 2-0 in the 40th minute when Etafia flapped at a cross from Bernard Parker and allowed Lehlohonolo Majoro to gleefully turn the ball home from close range.
Swallows started the second half strongly and had a couple of early chances for Siyabonga Nomvete that went a-begging. Had the Birds been able to take just one of them, it may have changed the course of the game.
Instead, just past the hour-mark, Chiefs extended their advantage when the excellent Masango netted his second, exchanging passes with Lebese in the penalty area before finishing crisply into the bottom corner of the net.
Lebese almost added salt to the Birds’ wounds just a minute later when he cracked a long-range shot against the crossbar. At this stage the home side looked like scoring every time they attacked.
Chiefs took their foot off the pedal in the last 20 minutes or so, though they remained disciplined at the back and made sure Swallows were not able to even sniff the possibility of a comeback.