It sees the Rockets leapfrog their opposition into seventh as Abafana Bes’thende slip to ninth, having started the day in seventh.
Arrows had the first attempt towards goal in the second minute. Sibusiso Sibeko was fouled on the far side and his free-kick was headed low and wide of the left-hand upright by Moyela Libamba.
Arrows took the lead with just seven minutes gone after having applied the early pressure as Sibusiso Sibeko controlled the ball well at the far post and squared the ball back for Moyela Libamba to tap in.
Galaxy equalised in the 36th minute. The initial cross came from Lindokuhle Mbatha on the near side across the face of goal as Thato Khiba swept home at the back post.
The Rockets edged themselves in front in first-half stoppage time as Lehlogonolo Mojela finished after being assisted by Solomon Letsoenyo to put Sead Ramovic’s side on top going into the dressing-room.
Galaxy were the side looking the more threatening as action resumed. However, there was little of substance created although there would be later.
With 20 minutes to go Themba Mantshiyane won a free-kick on the left for Arrows, who used the ball to press up as Sibeko fired a shot from the near side that was pushed wide across the face of goal.
Samir Nurkovic replaced Mbatha for Galaxy in the 78th minute and it proved an inspired substitution as the Serbian frontman extened the Rockets’ lead with a near-post effort that took a deflection on its way in.
There was a missed opportunity for Arrows to to pull a late goal back but Kagiso Malinga failed to find the target.