Van Zyl has won 13 times on the Sunshine Tour, and has 17 top-10 finishes on the European Tour, including two this season while playing on a medical exemption with a brace on his leg.
His bogey-free round included a tap-in seventh and final birdie on his last hole.
''Today was really a phenomenal round,'' he said after reaching a 10-under total of 203.
Maximilian Kieffer of Germany, also chasing his first European Tour title, was two back after shooting a bogey-free 65 and rising seven places.
Bernd Wiesberger of Austria was alone in third at 7 under thanks to a 66.