Phunya Sele Sele played host to the Chilli Boys at the Dr Petrus Molemela Stadium in the City of Roses.
The deadlock was broken four minutes before the half-time break and it was Tebogo Potsane, who hit the back of the net.
The Chilli Boys tried to restore parity with their long-serving forward Andile Mbenyane working tiressely upfront.
However, Celtic were able to hold on to their lead and they were leading 1-0 at the interval.
The home side continued to attack after the restart and they were awarded a penalty after Thabo Nthethe committed a mistake in the box.
Tshegofatso Mabaso then stepped up and hit the back of the net to make it 2-0 to Celtic, much to the delight of the home crowd.
Jabulani Shongwe was introduced in the 63rd minute as the Chilli Boys looked to pull one back.
However, the visitors found it difficult to beat Celtic goalkeeper Patrick Tignyemb, who made good saves throughout the game.
In the end, Celtic emerged 2-0 winners over Chippa courtesy of goals from Potsane and Mabaso.
Meanwhile, Lamontville Golden Arrows also began the new campaign with a win over Maritzburg United.
The Team of Choice welcomed their KwaZulu-Natal rivals Abafana Bes'thende at the Harry Gwala Stadium in Pietermaritzburg.
Maritzburg dominated the first half with Mxolisi Kunene and Siphesihle Ndlovu tormenting the Arrows defence with their skills and pace.
However, the visitors were able to contain the hosts and the score was 0-0 at the interval between Maritzburg and Arrows.
Arrows came back from the half-time break an improved side and they managed to break the deadlock in the 71st minute.
Danny Venter set-up Knox Mutizwa, who scored with a wonderful over-head kick to make it 1-0 to Arrows - beating Maritzburg keeper Richard Ofori.
The Team of Choice pushed forward in numbers in the closing stages of the game as they look to level matters, but they were left vulnerable at the back.
Maritzburg were punished by Lerato Lamola, who beat Ofori from close range to seal Arrows' 2-0 victory in stoppage time.