The resultant corner by Bernard Parker was cleared to Philani Zulu, who, with a short backlift, produced a power strike onto the crossbar. Then Parker chested into the path of Ekstein to lift a shot over.
Predictably, as Chiefs could not score, and Arrows produced a lone chance, the Durban team profited from it.
Knox Mutizwa's dangerous cross could only be cleared by Moleko's sliding clearance into the path of Sanele Mathenjwa, who advanced down the left and backheeled to Sibiya, who had plenty of work to do curling a classy strike round Daniel Akpeyi.
Chiefs continued to be confounded by matters of centimeters after the break.
Substitute Ryan Moon, on for Ekstein, saw a shot tipped over by Mbaeva. From Parker's corner the centreback pairing of Daniel Cardoso and Moleko picked out almost the exact same spot on the bar with a volley and a header.
Finally, when Chiefs got the goal they deserved it was buried with a simplicity – Moleko rising to power a header from substitute George Maluleka's corner – that made all Amakhosi's previous finishing failures appear immensely complicated.
Other Absa Premiership midweek results:
Tuesday April 23 2019:
Mamelodi Sundowns 3 - 2 Chippa United
Kaizer Chiefs 1 - 1 Lamontville Golden Arrows
Cape Town City FC 1 - 1 Highlands Park