The goals were scored with a brace from Clifford Mulenga and a goal by Thokozani Mshengu.
Former Arrows player Mshengu opened the scoring in the 33rd minute with a left-footed strike after being afforded too much space by the Arrows defence.
Poor defending by Arrows allowed Celtic to take shots at goal and left goalkeeper Helton de Rocha exposed on a number of occasions.
Celtic threatened from the beginning, passing the ball well in the midfield and taking long range shots in front of a retreating Arrows defence with Hlompho Kekana and Moses Spandeel coming close to scoring before Mshengu broke the deadlock.
Coach Ernst Middendorp made a change at half-time, bringing on Thamsanqa Gabuza for Dillon Sheppard in an attempt to add more width and pace to their attack.
Instead, it was Celtic who added another goal to their tally when Zambian ace Mulenga broke through the middle and unleashed a powerful strike that found the top corner to put Celtic 2-0 up in the 50th minute.
Arrows did not have much time to recover as Mulenga completed his brace in the 53rd minute, taking advantage of an indecisive Arrows defence.
Arrows’ first shot on target came in the 63rd minute via striker Katlego Mashego, but his attempt was saved by Patrick Tignyemb.
Overall, it was a frustrating start of the season for Arrows strikers Collins Mbesuma and Katlego Mashego as the Celtic midfield restricted their supply.