Fisher had an eagle and seven birdies, including a run of three straight in his back nine on the West Course at Royal Johannesburg and Kensington Golf Club. Sterne went bogey-free for the second consecutive round on the East Course.
The South Africans were 15 under at the European Tour event.
"My last three or four years have been good on the (South African) Sunshine Tour. But I need to get to the next level now," Fisher said. "It's been good for me in terms of the steppingstones I've taken in the last 10 years. But I've stepped on a lot of stones. I need to get to the top now."
Defending champion Branden Grace, No. 10 on the European money list, missed the cut after rounds of 72 and 70 for a 1-under total.