The log leaders, who are currently 16 points clear at the summit, tasted success in their 18th League game thanks to Mandla Masango's 60th minute header at FNB Stadium.
Aces, in mid-table, can feel hard done by as they twice struck the woodwork, with question marks raised as to whether the ball crossed the line on one of those occasions.
Chiefs dictated play early on, as Kingston Nkhatha and Bernard Parker fired unsuccessful shots on Jackson Mabokgwane's goal.
The visitors, though, came agonisingly close to scoring in the 19th minute, but Tendai Ndoro's strike in the box was superbly pushed on to the post by a diving Brilliant Khuzwayo. Moments later Ndoro had a shot cleared off the line by Man of the Match Mulomowandau Mathoho.
Soon after Nkhatha headed a Parker flick-on over from a corner, while at the other end Ndoro volleyed narrowly off target from an acute angle midway through the first stanza.
Amakhosi threatened again just before the interval, as Ugandan enforcer Ivan Bukenya headed a Siphiwe Tshabalala cross over from close range.
AmaZayoni started the second period strongly, and almost broke the deadlock in the 52nd minute as Aubrey Ngoma's dipping, left-footed effort beat Khuzwayo but not the crossbar. The Aces faithful thought the ball had crossed the line after hitting the woodwork, but referee Daniel Bennett and his assistants ruled otherwise.
Masango then struck the decisive blow on the hour-mark, as he headed in a right-wing cross from Nkhatha.
Masango could have made the game safe in the 78th minute but Mabokgwane dropped down smartly to deny the Glamour Boys attacker in a one-on-one situation.
Chiefs substitute Matthew Rusike nearly made an impact in the closing stages as his shot brushed the outside of the post. Mabokgwane, though, had it covered.