Fisher had an eagle and seven birdies, including a run of three in a row in his back nine on the West Course at Royal Johannesburg and Kensington Golf Club. Sterne went bogey-free for the second consecutive round on the East Course. They are 15-under at the European Tour event.
George Coetzee (64) is three shots back and two-time winner Charl Schwartzel (65) trails the leaders by five.
Defending champion Branden Grace, No. 10 on the European money list, missed the cut after rounds of 72 and 70 for a 1-under total.
Former Augusta State standout Jamie Elson also missed the cut after shooting 68-74.
CHAMPIONS TOUR: In Boca Raton, Fla., Bernhard Langer and Tom Pernice Jr. each shot 6-under-par 66 to tie for the first-round lead at the Allianz Championship.
Langer birdied three of the last four holes at Broken Sound. Pernice charged into contention after playing a six-hole stretch in 6-under.
Defending champion Corey Pavin, Roger Chapman, Fred Funk, Scott Simpson and two players making their Champions Tour debuts – Rocco Mediate and Bart Bryant – are a shot back after 67s.
EUROPEAN/AUSTRALASIAN TOURS: In Christchurch, New Zealand, Tamara Johns, Nikki Campbell and Sarah Oh each shot 3-under-par 69 to lead the 54-hole New Zealand women’s golf after the opening round.
The trio lead three players at 2-under, including the world’s No. 1 amateur, 15-year-old Korean-born New Zealander Lydia Ko.
Alison Walshe and Nontaya Srisawang were also at 2-under after the first round at the Clearwater Golf Club.