Usuthu started the match the better of the two sides and almost went ahead in the fifth minute when Mpho Maleka was played clear by Dennis Lota, but the striker’s shot was deflected wide of goal.
Celtic’s first real chance of the game arrived in the 15th minute when skipper John Maduka collected the ball outside the AmaZulu area, but his long range shot flew well wide of goal.
Mohammed-Awal Issa should have handed the hosts the lead in the 32nd minute when he received a good pass from Momikia Yemo, but the midfielder’s shot flew inches wide of the Celtic goal.
The visitors took the lead seconds before the break when Gary Goldstone scored from a corner by Grant Smit.
The match remained 1-0 at the break.
Celtic should have doubled their lead four minutes after the restart when Mark Amofah raced clear of the Usuthu defence and although his shot beat keeper Tshepo Motsoeneng, AmaZulu defender Peri Ariweriyai was able to clear the ball before it crossed the goalline.
The hosts should have drawn level in the 62nd minute when Celtic keeper Shuaib Walters parried Bafo Biyela’s shot straight at Maleka, but the striker somehow managed to put his effort over the bar from close range.
Maleka also hit the side-netting late on, as AmaZulu pushed everyone forward in a bid to draw level, but the Celtic defence held firm to secure their place in the next round.