The South African bogeyed the first two holes but did not drop a shot thereafter, claiming eight birdies between the sixth and the 17th to sit 17 under overall, two clear of American Hunter Mahan.
Mahan shot a best-of-the-day, seven-under-par 65 in a round that also contained eight birdies.
Also in contention were England's Brian Davis and Sweden's Carl Pettersson on 14 under.
For the second round in a row Davis did not drop a stroke, carding three birdies for a three-under 69, while Pettersson was five under for the day.
James Driscoll was fifth on 12 under, while defending champion Phil Mickelson was among a group of three players on 11 under.
Oosthuizen said on www.pgatour.com: "It's a great leaderboard behind me. It's going to be tough, but I feel like I'm ready for it."
Play began early on day three with 70 players yet to finish their second rounds on the back of bad weather on Thursday.
Jeff Maggert was the 36-hole leader on 12 under, but it could have been better had he not dropped a shot on the ninth - his last, having started from the 10th - for his first bogey of the tournament.
And that was a sign of things to come as he carded six bogeys on four-over third round, leaving him eight under overall in a tie for 14th, alongside, among others, Ernie Els and England's Lee Westwood.
Els, who needs to win to qualify for the Masters, said: "I needed to get to 10 or 11 under to really have a shot.
"I need a 62 or 63. It's tough to do on a Sunday, but you might as well give it a go."