Sandile Ndlovu scored for the Dube Birds and Musa Bilankulu netted for Abafana Bes’thende.
The first half was a dull affair and although Swallows enjoyed the better of the half, it was the visitors who produced the first real chance of the game, when Norman Smith shot over the bar from inside the area, following a good cross by Philani Shange in the fifth minute.
Former Arrows striker should have put the hosts ahead on the stroke of half time, but he shot straight at keeper Brendan Wardle from close range.
The half ended goalless.
Swallows took the lead in the 52nd minute when Ndlovu headed home from a corner by Patrick Thwala.
However, Arrows equalised 11 minutes later when Kagisho Dikgacoi headed the ball across goal for Bilankulu to head home from close range.
Arrows were boosted by the goal and almost went ahead in the 68th minute when Smith found himself in space inside the Swallows area, but his shot was superbly saved by Greg Etafia.
Abia Nale wasted a glorious chance to put Arrows ahead in the 72nd minute when he headed wide from close range following a good cross by Joseph Musonda.
Bevan Fransman almost secured the three points for Swallows in the final minute of the game when he latched onto the ball inside the area, but the Birds’ defender shot wide from six yards out.