The pair go into Sunday's final round locked on 19-under-par for the tournament, five shots clear at the top of the leaderboard.
Sterne is a five-times European Tour winner, but has not claimed a trophy since 2008, while Fisher is seeking his first win on the tour.
Fisher surged ahead on Saturday having gone out in 33 in his first nine holes, but three bogies coming home allowed his rival to stay in touch.
It could have been different after a fine approach to the 18th green left Fisher a 10-foot putt for eagle, while Sterne landed in the greenside bunker.
But an excellent save out of the sand gave Sterne a birdie and, when Fisher let the eagle chance slip, the opportunity to take the overnight lead was gone.
A quartet of players are five shots back, including twice winner Charl Schwartzel.
The 2011 Masters champion shot a bogey-free 68 to stay in the hunt, along with Chilean Felipe Aguilar (70), and home players Jaco van Zyl (67) and George Coetzee (70).
South African Garth Mulroy produced the round of the day, with a 65 which took him to 12-under for the tournament. The 2011 Joburg Open runner-up sunk eight birdies to go into Sunday tied for eighth place.
With thunderstorms predicted for Sunday afternoon, the tee-off times for the fourth round have been brought forward, with the leaders playing in a three-ball.
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