A first half of Tuesday's match Reneilwe Letsholonyane brace helped Chiefs to their eighth win of the season and stretched their unbeaten run to 11 league matches this season.
Chiefs bagged their third consecutive league triumph, after claiming wins over SuperSport United and Golden Arrows in their last two league encounters, while Swallows are now without a win in their last five matches across all competitions.
The hosts were in with the first chance of the match as early as the fifth minute, when the league's leading goalscorer Bernard Parker had his close-range effort neatly saved by Birds' goalkeeper Greg Etafia, who parried the shot out of danger.
Parker was in with another chance less than a minute later, when he picked up a loose ball inside the Swallows area and drilled his shot straight at Etafia, who did not have to move and clutched the ball to his chest.
Swallows had no answer and a minute later, Chiefs deservingly took the lead through Letsholonyane, who was yet to score heading into Tuesday's derby clash.
Back into the game
Siphiwe Tshabalala found Lehlohonolo Majoro inside the box, after making a good run over the halfway line and into the visitors' final third, before Majoro delivered a clinical ball across the goalmouth to an unmarked Letsholonyane, who made no mistake from three yards out.
Swallows eased their way back into the game after the early opener, with Katlego Mashego hitting a free-kick from outside the Chiefs area on target, but failed to beat goalkeeper Itumeleng Khune, who made a routine save to deny the visitors the equaliser.
The Birds continued to push for a goal and were rewarded in the 33rd minute, as Chabangu hammered in the equaliser.
A decisive flurry in the middle of the pitch saw Swallows come away with the ball and opened a space along the right flank, from which a pinpoint delivery was played to Chabangu, who beat Khune for his fourth league goal of the season.
Chiefs had an opportunity to hit back straight away, but some brave defending inside their own area, allowed Swallows to keep Parker from regaining the lead shorty after drawing level.
However, the hosts were not to be denied, as Letsholonyane scored his second of the night in the 38th minute, after some good work in the Chiefs' midfield allowed the ball to open up for Letsholonyane.
Denied by the crossbar
The Bafana Bafana midfielder picked his spot and slotted past a stranded Etafia, forcing the keeper to pick the ball up from out of his net for a second time in 30 minutes.
With their tails up, the Glamour Boys nearly went further ahead on the stroke of half-time, but Majoro was denied by the crossbar, as his header effort looked to have beaten Etafia.
Trailing at half-time, Swallows started the second period well and went in search of their second, with Bennett Chenene coming close in the 50th minute, but failed to beat Khune, who closed the Birds frontman down after Chenene made an excellent run down the left flank and deep into the hosts' area.
Chenene refused to let up and sent a hush around the stadium as he brought the scores level for a second time on the hour mark.
A slight lapse in concentration from the Chiefs defence allowed the striker to beat the defensive line and had a clear path to goal, before netting past Khune for his third league goal of the season.
Chenene's goal sparked a turnaround among the Chiefs ranks after a quiet second half, with Tshabalala coming close in the 69th minute.
In the thick of the action
The Amakhosi stalwart was put through on goal by second half substitute Kingston Nkhatha, but Tshabalala struck the effort with his weaker right foot and could not beat Etafia, who came out and made a solid save low down to keep the scores level.
Tshabalala was in the thick of the action shortly thereafter and forced a brilliant diving save from Etafia to keep out the midfielder's curled free-kick effort from just outside the Swallows area.
Letsholonyane came agonisingly close to scoring his hat-trick with 13 minutes left to play after Etafia was brought down by an aerial clash with Parker, leaving an open net for which to aim, but the midfielder narrowly missed the mark from 30 meters out.
With time ticking down, Khune made a spectacular save in the last minute of injury time to deny Katlego Mashego what looked like a certain winner, after the striker was put through on goal and had only the goalkeeper to beat.
Khune made a diving save at Mashego's feet to keep the scores level.
With less than a minute of injury time remaining, substitute Nkosi tapped in a Tshabalala corner to steal the lead with seconds left on the clock. – Sapa