Bernard Parker got the goal on 56 minutes as Amakhosi preserved their unbeaten record after 16 Absa Premiership games.
The victory, though, came at a cost as influential midfielder Willard Katsande was stretchered off with an injury in the first half at Peter Mokaba Stadium.
In the 15th minute Parker stole the ball in midfield and played Kingston Nkhatha through on goal – the Zimbabwean doing well initially to muscle his way into the box, but he failed to beat the keeper.
Mulomowandau Mathoho should have given Chiefs the lead five minutes later when he hit the crossbar with a eight-yard header after meeting a left-sided free-kick from Parker.
Chippa came close on the half-hour mark when George Akpabio used his strength to break into the Amakhosi box, but the goalkeeper denied him in a one-on-one.
The visitors should have had a penalty soon after, but Reneilwe Letsholonyane escaped punishment for tripping William Twala in the box.
Two minutes later Chiefs suffered a loss when Katsande had to leave the field injured and was replaced by Ivan Bukenya.
The half ended 0-0.
It came as no surprise that it was Parker who broke the deadlock in the 56th minute after some swift play saw him through on goal and chipping the onrushing keeper, 1-0.
The Amakhosi dominated proceedings thereafter, but they struggled to find that second goal.
Siphelele Mthembu should have scored for the Glamour Boys five minutes from time when he was put through on goal by Parker, but he was denied in a one-on-one with the keeper.