The goal was scored by Russel Mwafulirwa in the first half.
Chiefs had lots more possession throughout but never really troubled the Ajax keeper Hans Vonk. Ajax to their credit defended very well with Brazilian defender Eduardo Ferreira having a brilliant game.
Ajax took the lead in the 7th minute when Mwafulirwa dribbled into the box and scored with a shot from about 18-yards out.
Siphiwe Tshabalala nearly got the equaliser two minutes later when his shot went narrowly past the post.
Thuso Phala should have got the equaliser in the 22nd minute but missed the target from in front of goal.
Mabhuti Khanyeza had a chance to score but hammered his shot straight at Vonk in the 48th minute.
Craig Rosslee the Ajax coach was given his marching orders from the bench by the referee for interference in the 66th minute. He watched the rest of the game from the stands thereafter.
Chiefs were unable to crack the Ajax defence and the Cape side ran out winners against the run of play.
The win lifts Ajax to top of the table on 12 points but that could change if second placed Bloemfontein Celtic win against Moroka Swallows on Sunday. Chiefs are mid-table on 5 points.