Striker Sthembiso Ngcobo was handed a lone striker’s role in the absence of the injured Knowledge Musona and responded with two goals – his first in the League this season.
Former Amakhosi player Collins Mbesuma pulled one back for Abafana Bes’thende but the home team was unable to complete a comeback.
Siyanda Zwane was sent off in the 70th minute for a second yellow card.
The visitors started very fluently, with wide men Mandla Masango and Siphiwe Tshabalala finding plenty of space.
On nine minutes Tshabalala was put free down the right side of Arrows’ penalty area by Tinashe Nengomasha, but there was no one in a Chiefs shirt to turn home his peach of a ball across the face of the goal.
Two minutes later, with their first genuine attack of the game, Arrows sent overlapping right-back Siyanda Zwane into a shooting position and his low effort troubled Itumeleng Khune, who fumbled the ball and needed Valery Nahayo to clear.
Chiefs continued to find some joy in the wide areas, and midway through the first half Jimmy Tau cut inside from the right flank and curled a left-footed effort just wide of the far post.
A minute before the half hour mark Mthokozisi Yende floated a good cross into the box from the left, allowing Sthembiso Ngcobo to get a header on target, but it was comfortably saved by Helton da Rocha.
On the stroke of half-time Arrows created another overlapping opportunity for Zwane and his low cross flashed across the face of goal, just beyond the reach of Mbesuma.
The early stages of the second half saw the teams trade half chances in attack, and Chiefs soon made a substitution by replacing Masango with Abia Nale in the 52nd minute.
The former Arrows player had an almost immediate impact on the game, breaking free down the right and curling in a cross that da Rocha somewhat flapped at, allowing Ngcobo to head home at the back post.
And just past the hour mark Ngcobo made it 2-0, picking up a fine pass from Yende and firing a low shot into the bottom corner via the left hand of Da Rocha, who again could have done more to prevent to the goal.
The game seemed wrapped up for the Soweto side at 2-0, but former Amakhosi hero Mbesuma pulled one back in the 69th minute, finding the bottom corner with a well-placed shot after showing immense strength to brush off the attention of Nahayo.
Yet any real hopes Abafana Bes’thende had of a stunning comeback were crushed just two minutes after Mbesuma’s goal, as Zwane picked up his second booking and was shown a red card by referee Victor Gomes.
The KwaZulu-Natal team made a valiant effort to get something out of the game despite their numerical disadvantage, and Khune did have to make a couple of sharp saves from Mbesuma and Njabulo Manqana, but in the end Chiefs held out to win 2-1.