Both sides hit the woodwork in an entertaining, albeit barren affair at Lucas Moripe Stadium in Atteridgeville.
The result leaves Matsatsantsa in third place on the table with 36 points from 19 games - a point behind Bidvest Wits, and two shy of City, who have played an extra match.
Ajax remain 12th in the standings with 21 points from 20 fixtures - seven points above the drop zone.
The visitors threatened early on, as a backtracking Dean Furman nearly put the ball into his own net following a cutback from the right by targetman Nathan Paulse.
At the other end, SuperSport attacker Thabo Mnyamane kept young goalkeeper Jody February honest with a low shot from a tight angle in the 14th minute.
February had to be at his best on the half-hour mark, as he denied Mandla Masango from close range following a cross from the left by bustling hitman Kingston Nkhatha.
Soon after, Masango thumped a volley against the crossbar from outside the box as Matsatsantsa pressed for an opener before the break.
The Urban Warriors nearly stole ahead in the 62nd minute, as Bantu Mzwakali curled a shot from 30 yards out against the upright.
Ajax playmaker Mark Mayambela came close to snatching a winner in the latter stages as he triggered saves in quick succession from former Kaizer Chiefs keeper Reyaad Pieterse.
Mnyamane then tried his luck in stoppage time but was foiled by a fine stop from man of the match February.