Sterne followed up his opening-day 63 with another blemish-free round of 65 on Friday on the east course to join early leader Fisher Jnr on 15 under par for the tournament.
Fisher Jnr had looked set to take a comfortable lead into the third day after he shot a blistering 62 on the west course, just one stroke outside Charl Schwartzel's course record.
However, Sterne, who was runner-up to Stephen Gallacher in the Dubai Classic last week, continued his good run of form to stay in contention for his sixth European Tour title at the Royal Johannesburg and Kensington Course.
A birdie on the opening hole and gains at the fourth and seventh saw him quickly close ground on his compatriot before an eight-foot putt at the ninth saw him claim an outward score of 33.
Sterne then added birdies on three of the last four holes which saw him catch up with Fisher Jnr and repeat his effort from the opening day of finishing the round joint top.
"I did the right things and putted well. It's nice to not be behind going into the weekend," Sterne told europeantour.com.
"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 (Coetzee) is due a win, so it's a long way from over."
Fisher Jnr, who was named Sunshine Tour Players' Player of the Year two days ago, shot an eagle and seven birdies on the way to a nine-under-par round of 62 on day two.
"It was a great day out there," Fisher Jnr said. "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."
Coetzee completed the all-South African top three on 12 under par while home favourite Schwartzel fired 65 on the west course to tie for fourth place alongside compatriot Keith Horne and Felipe Aguilar of Chile.
And Schwartzel was not surprised with Fisher Jnr's strong performance so far in the tournament.
He said: "We played foursomes for South Africa Under-23s - I know how good he can be."
England's Tommy Fleetwood finished on nine under par for the first two rounds after he carded 66 on Friday to lie in a four-way tie for seventh while Scotland's David Drysdale and England's Richard Finch were another shot back in a cluster of nine players.