The 2010 Open champion's nine-under par round sees him at 16-under and clear of overnight co-leader Adam Scott who carded a 68.
The Australian was joined at 11-under by Open champion Ernie Els who matched Oosthuizen's 63.
South African Oosthuizen had a bogey at the second but then picked up birdies at the third and fifth before an eagle at the seventh.
A monster birdie putt on the eighth saw him draw level with Scott and that was the first of four consecutive birdies before he picked up further shots at 15 and 16.
“With this tournament I'm in a great position to win it but it's not even crossed my mind at the moment,” said the world number 11.
"There's still a lot of golf to be played and I need to put myself in a great position going down the back nine on Sunday.”
"I played the par-5s really well and I think I was 6-under on them today. The rest was down to putting really well. I gave myself a lot of opportunities for birdie, and hitting fairways, hitting greens, and if you make the putts, you shoot a low number."
Els had seven birdies on the front nine as he went out in 29 to join Scott who had three bogeys on the back nine.
Scott said making up a five-shot deficit over the weekend would be difficult with a quality player like Oosthuizen leading from the front.
The Australian kept pace with Oosthuizen with four birdies in his first seven holes but then fell back with three bogeys on the back nine.
"Its tough chipping around these greens," he said. "There are quite a lot of run-off areas and it's tricky to judge how your shots are going to respond when you hit chip shots."
Jason Dufner (66) and Ireland's Shane Lowry (68) are tied for fourth at 10-under-par while Dustin Johnson (68) and Phil Mickelson (69) are one back at nine-under on the Olazabal Course at Mission Hills.
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