Chiefs coach Stuart Baxter named a team with no out-and-out strikers. Kingston Nkhatha was ruled out due to sickness while Bernard Parker missed out due to a late injury – reportedly on the ankle he had surgery on, as a precautionary measure – but Siphelele Mthembu was on the bench.
The home side enjoyed the majority of the ball and created more opportunities than the visitors in the first half, but neither goalkeeper was kept too busy on a hot day in Cape Town.
Both Tefu Mashamaite and Siboniso Gaxa had to make cynical fouls on Tashreeq Morris and Travis Graham respectively, with the latter receiving a yellow card, while Keagan Dolly fired two shots off target from long range.
Bantu Mzwakali tested Brilliant Khuzwayo in the Chiefs goals with a direct free-kick from 24 yards in the 17th minute as a good diving save kept out the danger. Khuzwayo was then fortunate to get away with a poor punch from the resultant corner.
Six minutes from the interval Ajax created the best chance of the match when Mwakali dispossessed Willard Katsande high up the pitch before feeding Thabiso Nkoana, but the striker's shot was blocked by a brilliant recovery tackle from Morgan Gould.
Ajax assistant coach Ian Taylor was sent to the stands on the stroke of half-time, reportedly for continuously insulting the match officials, as Roger de Sa also exchanged a few heated words with referee Robert Smith.
The second half was a more exciting affair after Chiefs took the lead four minutes after the restart through Mashamaite. The centre-back got up to head home Siphiwe Tshabalala's inswinging free-kick from the right as Anssi Jaakkola could only get fingertips to the ball.
Ajax made a spirited attempt to get back into the match after Chiefs scored as Morris headed over the bar and Thabiso Nkoana turned and shot wide of goal. Roger de Sa also replaced Keagan Dolly with Nathan Paulse as Ajax went more direct.
George Maluleka and Reneilwe Letsholonyane tried shots that went high and wide as Man of the Match Tshabalala started pulling the strings more for Chiefs with some dangerous crosses and clever through-balls.
Ajax could not find an equaliser, so Chiefs' eighth straight League win means they have now broken Mamelodi Sundowns' record of 14 consecutive domestic wins achieved in 2007 as they have won 15 matches in a row including the two wins at the end of last season.
Amakhosi also moved 10 points clear of the four chasing teams at the top of the Absa Premiership table.