Two first half penalties from Limbikani Mzava had put Arrows in command at the break, but after Leonardo Castro scored on the hour mark.
The home team found themselves under increasing pressure and had to work very hard defensively to secure victory, their first in four matches.
Lashing rain, a thunderstorm in close proximity, and a very poor playing surface made for some tricky conditions in KwaMashu.
The Soweto side did manage to get some promising early balls into the box, but Arrows keeper Maximilian Mbaeva was up to the task as he made some important interventions.
However, when a Chiefs attack in the 25th minute broke down inside the Arrows half, the Durban side countered with blistering pace and as Lerato Lamola entered the Amakhosi box, he drew a clumsy challenge from Erick Mathoho.
Whether Mathoho actually did enough to concede a spot kick was very debatable, but referee Welcome Setloboko decided there was enough of a foul to point to the spot.
Abafana bes’Thende captain Mzava stepped up to take the spot kick in the 27th minute and did just enough to beat Chiefs keeper Itumeleng Khune, who got a hand to the ball.
Incredibly, a similar situation was to unfold just four minutes later when Teenage Hadebe went sliding in recklessly on Siboniso Conco, whose feet were taken out from underneath him just inside the box, for what looked a more clearcut penalty.
Once again Mzava took the responsibility, and again his spot kick went low and to Khune’s right, the keeper again getting contact on the ball but failing to keep it out the net; 2-0 to the hosts after 31 minutes.
Amakhosi battled to mount any sort of a comeback in the first half and it could have been 3-0 to Arrows four minutes before the interval, when Conco raced clean in on goal, but he lost his cool at the vital moment and Khune was able to charge off his line and make a brave block.
Chiefs showed good intent after the break, and after a couple of half chances, they pulled one back in the 60th minute, Castro poking the ball into the net from close range after Mbaeva had fumbled a cross and a goalmouth scramble had ensued.
The game now balanced on a knife-edge, the Glamour Boys had the next chance on goal in the 76th minute, but just as Khama Billiat was about to strike from close range, Nkanyiso Cele got back to make a brilliant last-ditch tackle.
Billiat was at it again eight minutes later when he latched onto a flick from Castro, but Mbaeva made a wonderful save to tip the ball over the bar.
More pressure followed from Chiefs as Mathoho fired narrowly wide with a snap shot in the box before George Maluleka went close with a 90th minute free kick.
Deep inside the eight minutes of added time, the visiting team were again close to scoring when Khune stepped up to take a free kick which dipped and swerved inches wide, in what was the final chance of a very entertaining night’s action.