Amakhosi, who face Downs at the same venue on Saturday, prevailed through second-half goals from Mulomowandau Mathoho and Kingston Nkhatha.
Chiefs dominated possession from the onset but were unable to break down a resolute Arrows outfit in the opening stanza, with ex-Glamour Boys goalkeeper Arthur Bartman making a fine save at his near post to deny Siboniso Gaxa just before the recess.
The hosts, however, stole ahead in the 53rd minute, when Mathoho headed in a superb inswinging free-kick from the right by Siphiwe Tshabalala.
Stuart Baxter's men doubled their advantage 16 minutes later, as the hard-working Nkhatha squeezed his left-footed shot past Bartman from a tight angle after linking up nicely with Bafana Bafana fullback Tsepo Masilela.
Chiefs played out the latter stages in relative comfort to hand ailing Abafana Bes'thende their sixth straight defeat in the League.