In a drab contest, United's David Booysen was sent off with 20 minutes to go after receiving a second caution at Cape Town Stadium.
The result sees Ajax and United move up to second and third on the log respectively, but they could lose those positions depending on results in Sunday’s two League matches.
Ajax settled the quicker of the two teams and began to dominate the match. However, they were unable to create any clear-cut chances from which to test goalkeeper Virgil Vries.
The goal-minder was called upon midway through the first half to parry away a good cross from Milton Ncube that would otherwise have found the head of Nathan Paulse and in all likelihood ended in an Ajax goal.
Maritzburg offered a sporadic threat on the counter attack and from set pieces. Perhaps their best chance arrived just after the half-hour mark, with striker Terrence Mandaza given a sight of goal, only to shoot straight at Anssi Jaakkola.
Ajax suffered a blow to their defence when young Bafana Bafana centre-back Rivaldo Coetzee had to be withdrawn due to injury in the 40th minute. Aidan Jenniker replaced the 18-year-old.
The visitors almost claimed the lead early in the second half through Ghanaian defender John Paintsil, who hit the top of the crossbar with a header from a set-piece. Ajax winger Bantu Mzwakali then showed some great skill and speed to create a chance for himself in the 56th minute, but he only managed to shoot straight at Vries.
Seven minutes later the aerial power of Paulse nearly broke the deadlock, with the striker providing a towering header from a hopeful long ball out of Ajax’s defence that almost looped into the goal, but ended up nestling on the top of the net.
By this stage the Urban Warriors were well on top and they were given a further boost when the Team of Choice was reduced to 10 men – defender Booysen picked up his second yellow card in the 70th minute and was sent off for an early shower.
On 81 minutes Ajax substitute Clifford Mulenga almost produced a wonder long-range goal, but his left-footed shot from 25 metres out drifted just wide of Vries’ left-hand post.