Thamsanqa Gabuza scored the first goal late in the first half, with Thanduyise Khuboni adding the second just after the break from the penalty spot.
The Dube Birds created a number of chances in the first half, with Oscar Machapa forcing a great save from Helton Da Rocha in the ninth minute, while Lerato Chabangu did the same in the 16th minute.
Swallows continued to put a lot of pressure on the home side, with Siyabonga Nomvethe and Lerato Chabangu combining well on the left flank, but they failed to make it count, partly due to some good cover defending from Golden Arrows.
The opening goal arrived three minutes before half time when Siyanda Zwane played a brilliant low cross from the right flank to find Thamsanqa Gabuza, who came sliding in to bury the ball home.
Arrows were awarded a penalty four minutes into the second half when Giorgi Nergadze was adjudged to have brought down Collins Mbesuma inside the penalty area.
Captain Thanduyise Khuboni made no mistake from the spot, sending Greg Etafia the wrong way to hand his side a two-goal lead.
Arrows almost put the result beyond doubt in the 59th minute when Thamsanqa Gabuza played a cross from the left and Mbesuma's neat touch directed the ball towards the far post, but somehow Etafia was able to get a hand on the ball just before it went over the line.
Gordon Igesund's men continued to search for their opening goal to reduce the deficit but at the same time made themselves vulnerable against an Arrows side that used their wings and pace to stretch the defence.
However, Muhsin Ertugral's side held on to secure their second straight league victory and their first at home under the Turkish coach.