City compounded a miserable start to the new season for Celtic, who sacked coach Serame Letsoaka at the weekend and had co-coaches John Maduka and Lehlohonolo Seema in charge for this match.
It was a deserved win for City at Cape Town Stadium, though Celtic had their chances, particularly in the first half.
But Majoro’s excellent instincts in front of goal allowed him to nip in as a back-header from Wandisile Letlabika dropped short of goalkeeper Ayanda Mtshali and the former Bafana Bafana forward opened his account for the club.
Celtic could have been 2-0 up by then as Atusaye Nyondo poked wide of a gaping goal and then saw his header come back off the crossbar with City goalkeeper Samora Motloung, a surprise pick ahead of Shu-Aib Walters, well beaten.
There were fewer chances in the second half as City dominated possession and at times were easy on the eye, only for their moves to break down in the final third.
City handed a debut to Ghana defender Joseph Adjei off the bench as coach Eric Tinkler resorted to a back five for the closing stages of the game.
Tinker's side are next in action against Baroka FC in the quarter-finals of the Telkom Knockout on Saturday, while Celtic will have a free weekend.