Fisher had an eagle and seven birdies in a 9-under-par 62 on the West Course at the Royal Johannesburg and Kensington Golf Club. The course record is 61, held by Charl Schwartzel.
Sterne played the tougher East Course Friday and turned in a bogey-free, 7-under 65. He and Fisher are at 15-under 128, three up on the field with 36 holes to play.
The tournament is conducted on the East and West courses the first two days with the final two rounds at the East Course.
George Coetzee, on the East Course, shot a second-round 64 and is alone in third at 12-under. Schwartzel, who had a West Course 65, is tied with Keith Horne and Felipe Aguilar for fourth at 10-under for the tournament. Horne and Aguilar each shot 66 on the East Course.
Fisher had an eagle at the par-5 second hole and added birdies at Nos. 3 and 9 but he really made his move with a 5-under 30 on the second nine. That included three consecutive birdies over Nos. 15-17.
Sterne opened with a birdie and mad his turn at 4-under. He closed with three birdies in his final four holes.
McPhee, Cokas 'working on their marriage' after affair
LGBT community has 'bullied the American people': Bachmann