Arrows, who humbled Platinum Stars 4-1 at the weekend, prevailed this time through Bongi Ntuli's 65th minute goal at Princess Magogo Stadium.
Both sides had chances to find the back of the net but it was the hosts who made it count midway through the second half.
Abafana Bes'thende searched for the early opener but Ntuli fired narrowly over the crossbar in the seventh minute before Festus Mbewe headed straight at Ronwen Williams two minutes later.
Ntuli used his pace to create two more good chances but Williams used his legs to deny him at the near post in the 18th minute, before he shot at the side-netting in the 26th minute.
Philani Shange broke the offside trap to latch onto a lobbed pass in the 35th minute but the Arrows winger shot wide of the far post with the goalkeeper off his line.
Arthur Bartman was then called into action at the other end, blocking an effort from Thuso Phala in the 36th minute, before making a comfortable save to deny Dino Ndlovu three minutes later.
Arrows came close to taking the lead from a free-kick on the stroke of half time but Thato Mokeke made a good clearance on the line to keep out Shange’s effort.
SuperSport had opportunities early in the second half with Bennet Chenene shooting over the crossbar in the 47th minute while David Mathebula's free-kick was palmed away by Bartman in the 58th minute.
Arrows opened the scoring just past the hour-mark as Ntuli controlled a pass from Chris Katongo before firing home from close range.
The hosts spurned two good chances to double their lead when Nkanyiso Mngwengwe headed wide in the 71st minute, while Manti Moholo shot wide from inside the box nine minutes later.
Both teams were denied by the woodwork in the closing minutes as Sibusiso Khumalo and Rudolf Bester struck the upright.
Arrows stay in 16th place on the table with 21 points from 28 matches, while SuperSport United are fourth with 41 points from as many fixtures.