The 31-year-old Sterene, who is based at the Royal Johannesburg course, added a second round 65 to his opening 63 to sit at 15 under par.
Fisher matched him with a sparkling nine-under-par second round of 62 - which included seven birdies and an eagle - that put him alongside Sterne and three shots clear of third-placed George Coetzee.
“It was a great day out there,” said Fisher, last year’s third-place finisher. “Everything just happened for me and I sank the putts I needed to sink.
“I was happy and patient with myself – walked slow and did everything slow – and it was just a good day.”
Last week in Dubai Sterne led at half-way before finishing runner-up to Stephen Gallacher, and he is determined to win this week.
“I did the right things and putted well,” he said. “It's nice to not be behind going into the weekend.
"It won't be easy on the weekend. The players that are five or six back can catch us as well. Charl's there, George is due a win, so it's a long way from over."