Celtic took the initiative early on and opened the scoring when Ronald Pfumbidzai powered through the box to slot his shot underneath King Ndlovu.
Leopards looked for a swift response as Tshwarelo Bereng produced a devilish curling effort for the away side which fizzed past goal, while Lifa Mhlongo and Mwape Musonda were both thwarted by Patrick Tignyemb.
Leopards came knocking again just before the interval when the league's top scorer, Musonda, broke behind the Celtic defence, but his shot was again saved by Tignyemb.
The second half was a much tighter affair with both sides not making any inroads, which prompted Leopards coach Dylan Kerr to introduce Thokozani Sekotlong for his debut on 57 minutes.
In the 72nd minute, Leopards' task was made even harder when Khuliso Mudau was handed a second yellow card for a foul on Tebogo Potsane as the visitors had to play the final 20 minutes with ten men.
Celtic eventually killed off the contest through Victor Letsoalo, who found himself one-on-one with Ndlovu for an easy finish with eight minutes left.
One minute later, Letsoalo completed his brace with a delicate chipped effort to round off an impressive victory for Celtic.
Celtic: Tignyemb, Letlabika, Pfumbizai, Rikhotso, Maema, Tani, Mabasa, Mashikinya, Dlamini, Phalane, Baloyi.
Subs: Dambe, Letsoalo, Shikweni, Masuku, De Jongh, Sam, Potsane.
Leopards: Ndlovu, Mudau, Zulu, Munganga, Masia, Nene, Bereng, Tshepe, Musonda, Mhlongo, Hlongwane.
Subs: Muleka, Ndou, Mashoene, Mokoena, Kapinga, Sekotlong, Mahangwahaya.