Brown struggled early but recovered with three birdies on the last five holes for a round of 72 and an 11-under-par total of 205.
Syme bogeyed the second but three birdies on the back nine ensured an impressive third-round 67 in tough conditions on South Africa's east coast.
"I thought I putted really steady today although it’s always tricky in the breeze," said Syme.
Andy Sullivan from England carded a best of the day 66 for a share of third place on nine under par, alongside American James Nicholas and South Africa’s Robin Williams.