Both birdied the final hole for a 19-under total of 196 at the Royal Johannesburg & Kensington GC.
Sterne and Fisher exchanged the lead on several occasions during the round, setting up an intriguing final day.
"A bit of nerves set in there," Fisher said. "You try not to think about the lead, but it's there in front of you. I was a bit jumpy with the swing and wasn't waiting at the top, so I hit a few bad shots there. But I came back nicely with a few birdies."
Sterne had birdies at Nos. 6 and 7 before Fisher went to the turn with three straight birdies.
On the back nine, Fisher recorded consecutive bogeys and Sterne birdied the 11th before Fisher drew even again. Both players dropped shots at No. 15 before finishing with birdies on the par-5 18th.
Schwartzel moved up the leaderboard with a bogey-free round that included four birdies.