The pair were on five-under-par through 10 holes, two strokes ahead of Englishman Danny Willett and Charl Schwartzel on three-under, while five golfers were on two-under – veteran Miguel Angel Jimenez, Kiradech Aphibarnrat, Jamie Donaldson, Brooks Koepka and Alexander Levy.
Both Coetzee and Fisher relied on precision iron play to collect five birdies, with no bogeys, and they vaulted into the lead around the turn with a pair of birdies on the par-five ninth and 10th holes.
Thailand’s Aphibarnrat had provided plenty of entertainment for the Sun City spectators as he claimed an early share of the lead when he played the first five holes in three-under-par, with four birdies and a bogey. Coetzee claimed birdies on the first three holes to provide early cheer for those hoping for a first South African winner of the Nedbank Golf Challenge since Trevor Immelman in 2007.
The opening holes of the European Tour event held few worries for the golfers as Joost Luiten, Dawie van der Walt, Stephen Gallacher and Willett all picked up an early brace of birdies.
Van der Walt, in the field by virtue of winning the 2013 Sunshine Tour Order of Merit, made the fastest start of all by birdieing the first hole and then chipping in for eagle on the 520m par-five second, but he could not pick up any more shots on the next three holes, dropping a stroke on the par-three fourth after finding the greenside bunker and then leaving his chip way past the hole. Another bogey on the eighth left him on one-under-par, alongside Gallacher.
A disastrous triple-bogey seven at the 11th saw Luiten slump to one-over-par for his round.
Thomas Bjorn, the defending champion, started where he left off last year in his brilliant final-round 65 by birdieing the first hole, but his wayward hitting saw him go out in three-over 39 as he collected a double-bogey and two bogeys thereafter.
South African Tim Clark, who teed off in the first group, set the early pace with birdies at the first two holes, but he then lost his way with a bogey at the fifth and a double-bogey at the tricky par-four eighth, before getting back under par with birdies at the 10th and 11th holes.
Aphibarnrat, a Sun City rookie, showed that he had all the information he needed on the Gary Player Country Club course as he started birdie-birdie, but Coetzee stayed in contact.
The conditions at Sun City were close to perfect, a slight breeze helping to offset the heat, and the golfers took advantage with 17 of them under par.