After drawing away to Ajax Cape Town and shocking Kaizer Chiefs in their first two league matches, Gordon Igesund's side have now gone three matches unbeaten and look nothing like the relegation material many pundits predicted them to be.
The season still has a long way to go, but five points from three games is a fine haul for a newly promoted team and they will look forward to the rest of the campaign with confidence.
Celtic, meanwhile, can at least take some solace from claiming their first point of the season, having lost their first two matches to Mamelodi Sundowns and Thanda Royal Zulu.
After a slow start to the game, it was Celtic who threatened to break the deadlock midway through the first half and Mark Mayambela saw his 12-yard shot turned round the post by United goalkeeper Hunter Gilstrap.
Four minutes later Gilstrap made a comfortable save from Geoffrey Sserunkuma's header after Moses Spandeel had worked some space to cross for his fellow forward.
Sipho Mngomezulu, who had scored a long range goal against Kaizer Chiefs in Maritzburg's last outing, again tried his luck from a fair distance in the 31st minute, but this time Celtic 'keeper Shu-aib Walters watched the ball fly wide of his upright.
Celtic's Solomon Mathe also saw fit to have a long-range effort at goal, shooting from 25 yards out just a few minutes before the half time break, but again Gilstrap made a straightforward save.
Four minutes into the second half, Spandeel saw his effort from the right side of the penalty area go wide of goal, and then United's John Arwuah was unlucky to see his close range header pass the wrong side of the post.
On 55 minutes, striker Brice Aka got on the end of Junior Khanye's free kick, but Walters was not unduly troubled by the Ivorian's header. It was a similar story nine minutes later from United substitute Lucky Maselesele.
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