The 36 year old is a Major Champion with four of his other seven European Tour wins coming in South Africa but his home Open is still missing from his trophy cabinet.
He entered day three at Randpark Golf Club two shots behind countryman and fellow Major winner Charl Schwartzel but produced a masterclass of mid-range putting and bunker play to move to 14 under and lead the way.
Schwartzel was in the group in second alongside England's Matt Wallace and Zambian Madalitso Muthiya, with a group of eight players then six shots off the lead.
Oosthuizen has three top tens in this event - which he is playing for the first time since 2010 - as he seeks a first victory in almost three years.
“It was tough again but I played well,” he said. “I hit a few bad drives where I was left but on 12 I fixed it quickly and then rolled the putter nicely today.
“I've been putting well for a long time now. Yesterday I couldn't make anything and today the makeable ones went in.
“18 more holes of good golf and I just need to take one shot at a time.”
Schwartzel has six top fives in his home Open including two runner-up finishes, while Wallace is seeking a remarkable fourth win of the calendar year.
World Number 1330 Muthiya overcame two double-bogeys - including a double-hit - in his level-par 71 and would become the first ever Zambian winner on the European Tour with a victory on Sunday.
Oosthuizen holed a long putt for birdie on the opening hole and that soon had him in a share of the lead as Schwartzel went left off the tee and missed a short putt for par to drop to 11 under.
Muthiya was just off the green with his second into the second but took the putter out and holed a very long right-to-lefter to hit the front on his own.
A Schwartzel three-putt on the third then dropped him to ten under and he was joined there by Wallace, who played the par five fourth in textbook fashion after holing an eight-footer at the third.
Oosthuizen also made the most of the fourth but dropped a shot on the next and Muthiya lead by two when he capitalised on the par five.
The 35 year old then had a rotten stroke of luck on the par-three fifth, missing the green and hitting a poor chip before having a double-hit when trying to play a fairway wood from the fringe.
The resulting double-bogey dropped him back to 11 under and Oosthuizen moved ahead after a beautiful pitch into the sixth.
Wallace turned in 33 after almost driving the ninth but Muthiya was heading in the wrong direction, making a double-bogey on the tenth after finding the sand.
Oosthuizen made smart par saves on the tenth and 11th and got up and down from the sand on the 12th but Schwartzel also birdied the par five to keep the gap at two.
The leader then put his foot down, again getting up and down from sand on the par-five 14th and holing from 15 feet on the par-three next to lead by four.
Muthayi needed a response to get himself back near contention and he produced one, holing a monster putt on the 11th and making the most of the two par fives on the back nine to get back into a share of second.
Oosthuizen's incredible run of scrambling from the sand ended on the 17th with a bogey and that was just three ahead of Wallace, who holed a long putt on the last for the third birdie of a back nine that also contained three bogeys.
Four-time Major Champion Ernie Els is looking for a sixth win at this event and he was in the group at eight under alongside fellow South Africans Branden Grace and Jbe Kruger, Scot Robert McIntyre, German Bernd Ritthammer, Dane Jeff Winther, Brazilian Adilson da Silva and Zimbabwe's Mark Williams.