Zakhele Lepasa (30', 53') scored both of Matsatsantsa's goals as Knox Mutizwa netted a 76th minute penalty for the visiting team.
It was SuperSport who started the tie the stronger of the two teams with Patrick Maswanganyi close to a very early opener with a shot that flew just past the Abafana Bes'thende left upright.
Siphesihle Ndlovu was then wayward with a half-chance minutes later before Thapelo Maseko saw his 17th minute goal-bound effort deflected wide of the target.
The home team remained in the ascendancy throughout the first half with Grant Margeman and Thamsanqa Gabuza both a threat, but it was Lepasa who was to leave his mark as he picked up a good Maseko pass and slotted home on the half-hour mark.
Lepasa could have added a second before the break but Arrows held firm, while they began to create a few chances of their own in the second half, most notible with Ntsako Makhubela firing marginally wide on 48 minutes.
But Lepasa was on target again soon after with a well-placed effort in the top corner of the Arrows goal, following a pin-point Siphesihle Ndlovu set-up.
Arrows threw on a number of substitues on in a bid to turn this tie on its head, and were a more lively side for the remainder of the tie, with Thubelihle Magubane coming close before Mutizwa netted from the penalty sopt after Divine Lunga was fouled in the box.
Bongumusa Nkosi and Magubane both had chances to find a late equaliser for Arrows, but SuperSport held on for the win, to remain five points clear of third-placed Orlando Pirates and Kaizer Chiefs in fourth.
Arrows ended the evening in 12th place with 25 points from 22 games played.