Celtic's goal was scored by Prince Hlela in the 76th minute.
Both sides started slowly, but that was to be expected as neither had played a match for roughly three weeks.
The best chance of the half came early, when after some neat passing Bennett Chenene found himself with the ball, unmarked and 12-yards out from goal. His shot, however, was a poor one as he pulled it narrowly wide with the goal at his mercy.
The home side then came closest to finding the opening goal twelve minutes later when Nathan Paulse rose highest to meet a Prince Hlela cross, but his powerful header struck the woodwork and bounced away from danger.
At the other end of the park Patrick Tignyemb was in fine form for Celtic between the sticks. He produced a fantastic save in the 25th minute to deny Arrows’ Vusumuzi Vilakazi, tipping his thunderous shot round the post.
Moses Spandeel also came close to breaking the deadlock seven minutes from the break when his 20-yard shot shaved the wrong side of the upright.
Celtic dominated going into the second have, and Hlela snatched the lead when he headed home an in-swinging Clifford Mulenga corner.
Arrows tried to find their way back into the game, but their hopes of finding an equaliser though were dealt a severe blow when Joseph Musonda was sent from the field for a horrible tackle and then some abusive language towards the referee.
When the game looked done and dusted, Arrows managed to find a dramatic equaliser. In virtually the last move of the game Gabuza fired his side level from six yards out, after being set through on goal by Manqana.