The 33-year-old Fisher strung together seven birdies and an eagle on the less challenging West Course at the Royal Johannesburg and Kensington Golf Club to finish on 15-under 128 alongside joint overnight leader Sterne (65).
"It was a great day," Fisher told reporters. "Everything just happened for me and I sank the putts I needed to sink.
"I was patient ... I walked slowly and did everything slowly."
Fisher and Sterne were three shots ahead of third-placed South African George Coetzee (64) who is also looking for his maiden European Tour victory after a string of near misses.
World number 18 Charl Schwartzel, the highest-ranked player in the tournament, burst through the field with a 65 as he grabbed a share of fourth position on 133 with Chile's Felipe Aguilar (66) and South African Keith Horne (66).
"It won't be easy over the weekend," said the 31-year-old Sterne. "The players who are five or six back can catch us.
"Charl's there, George is due a win, so it's a long way from being over."
Former U.S. Masters champion Schwartzel is making his first appearance after injury had kept him out for seven weeks.
"I had five and a half weeks of doing nothing and then I started practising a bit," he said.
"My ball-striking is good enough but I'm not putting as well. Those short ones are the ones you have to make to win tournaments."
The players will now use the more difficult East Course for the last two rounds.
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