Gallants were the side enjoying the better of the possession in the opening exchanges and almost took the lead with 25 minutes gone when Arrows goalkeeper Sifiso Mlungwana missed his punch before the ball was cleared off the line by defender Divine Lunga.
The visitors had a great chance to convert their dominance into a lead against the run of play via the penalty spot five minutes before half-time. Katlego Otladisa drew the foul in the penalty area and Celimpilo Ngema's spot-kick was saved initially but the diminutive midfielder headed home the rebound.
Arrows equalised five minutes after the break. Lehlohonolo Nonyane handballed and Knox Mutiwa's set-piece delivery was diverted into the roof of the net from close range by Nqobeko Dlamini.
Mutizwa turned provider again on the hour mark when he released Pule Mmodi, who found the bottom right corner with precision on his stronger right foot as Arrows took a 2-1 lead.
It was proving to be a virtuoso performance from the Zimbabwean striker as he grabbed Abafana Bes'thende's third with a well-executed finish.
Gallants made it a nervy final ten minutes when they netted through a header from Ranga Chivaviro from a set-piece, but Arrows held on to claim the three points.