The tournament has suffered three lengthy suspensions due to heavy thunderstorms but with a rare dry day at the Serapong Course ending without an interruption, the Dane sits at the top of the leaderboard on nine-under after 39 holes.
The Ryder Cup vice-captain has been bogey-free for 27 holes and the 41-year-old attributed his low scoring to pinpoint accuracy with the driver.
"This course doesn't really offer you that many wedges," he said after the completion of his second round.
"Your mid-irons have to be on but driving is also essential on this course. You need to get off the tee well and I've done that for two days, and long may it continue."
Chris Wood is hot on Bjorn's heels in second place after the Briton followed up his second round six-under 65 with another birdie in the three holes the leading group played in the third round to move within a shot of the Dane.
George Coetzee registered a second round eight-under 63, the lowest score of the week, to surge up the leaderboard and the South African remains two behind Bjorn after cancelling out a bogey with a birdie over the early holes of his third round.
Starting on the 10th hole, Coetzee's second round was highlighted by a run of six birdies in eight holes but the 26-year-old lamented a string of missed opportunities that could have put him in a stronger position.
"When I was standing on ninth green (his last), I thought to myself, 'I lipped out on five, six, eight and nine.' If I'd made all of them it could have been 10 in a row," he said.
Italy's Francesco Molinari and first round leader Chapchai Nirat of Thailand share fourth spot on six-under, while a group of seven players, including three-times champion Adam Scott of Australia are a further shot adrift.
World number one Rory McIlroy admitted to being frustrated by the regular weather delays but the Briton moved into contention at four-under after nine holes of his third round despite a slow start to the tournament with back-to-back 70s.
The Northern Irishman roared out of the blocks in the third round and an eagle on the par-five fourth took him to within four shots of the lead but a double-bogey after finding the water on the sixth stalled his charge.
He recovered quickly with a birdie on the next and with 27 holes still to play, McIlroy will fancy his chances of at least claiming a top-three finish that would secure the European Tour order-of-merit title with two events to spare.
"I played well when we got back out there, got off to a good start then unfortunately made a mistake on the sixth but got one straight back on the seventh," McIlroy said.
"Two under through nine was a pretty decent effort, but I probably need a few more birdies tomorrow morning to get myself within a few shots of the lead going into the fourth round... if it ever happens, that is."
A regular on any highlight reel, Phil Mickelson produced a sublime chip between two palm trees on the 18th hole of his second round that rolled to within six feet to ensure he got the birdie he needed to make the cut at one-over par.
"It was one of the best chips," the American said. "I had to go through the trees and run it up the hill. I hit it really well and made birdie and hopefully have given myself a chance."
Mickelson opened his third round with three birdies and a bogey to climb up to a tie for 37th on the leaderboard at one-under par.
Malaysia's Danny Chia conjured up a miracle shot of his own to also make the cut when he aced the par-three 17th to become the third player in as many days, after Edoardo Molinari and Juvic Pagunsan, to register a hole-in-one.