Both teams made their intentions known in the early stages by staging some strong attacking moves.
United goalkeeper Malcolm Jacobs was a busy man in the opening few minutes, while at the other end, the First Division side ensured they made their presence felt by keeping the Celtic defence on their toes.
With both sides determined to get forward, something had to give and it was Celtic who got the opening goal in the 27th minute when Burundian striker Fiston Abdul Razak scored.
Celtic went into the halftime break with a narrow one-goal advantage, but the overall quality and superiority of the PSL team was always going to tell.
And it did eight minutes into the second half when the energetic Razak netted his second and Celtic cruised into a 2-0 lead.
Visitors United also looked to their bench for some inspiration, with Thabo Mohlala replaced by Thamsanqa Masiya.
With five minutes to go, Inky Masuku pulled one back for United to make it 2-1, but it was too little, too late from the First Division campaigners.
Celtic were able to play out the final moments and go on to register a well-deserved victory.
African News Agency (ANA)