The South African and Australian - both runners-up in Major Championships this year - carded rounds of seven-under-par 65s over the Olazábal Course to share pole position on Thursday.
Former Open champion Oosthuizen, who was beaten in a play-off at this year's Masters Tournament by Bubba Watson, had seven birdies in his round including a 15-foot effort on his final hole of the day, the par five ninth.
That looked good enough for the first round lead until Scott hit a stunning second shot to 12 feet at the same par five and sank the resulting eagle putt.
Watson and another left-handed American who owns three Green Jackets, Phil Mickelson, are joined by last week's BMW Masters champion Peter Hanson and Shane Lowry in third place on six under par.
Oosthuizen, whose two European Tour wins this season include victory in Malaysia a week after his Augusta heartbreak, admitted he had not expected to get off to such a good start.
"I don't think I saw a really low number out there but once you look at the leaderboard and see the guys are firing it up, all of a sudden you started seeing birdies," said the 30-year-old.
"I played well - I made five birdies on the par fives, and that got the round going, and then I made two more birdies. I hit a few bad iron shots, but made good up-and-downs for pars and just glad to have a bogey-free round, I'm always happy with that.
"There are three rounds left and a lot of golf to be played. The main key is to try to put myself in a spot to win it on Sunday. If I can keep doing what I'm doing on the par fives and hitting fairways, you've got a good chance."
Scott was delighted with his finish as he chases a second WGC title after claiming last year's WGC-Bridgestone Invitational.
"It was a solid day that all of a sudden turned into a really good day," said the dashing Australian, who has won numerous titles in Asia.
"I hit a lot of good shots, and they ended up finishing close on the last couple holes and I took advantage of that.
"With five par fives, it sets up well for my game, and the plan is to just take advantage of the fives and hopefully hang in there with the leaders all week."
Mickelson, seeking a third victory in the event, matched Scott's eagle on the ninth, in his case from 25 feet, and said: "My game feels really good. It's gotten better each week since the PGA Championship and hopefully I can carry on - I certainly feel confident that I will be able to."
Watson mixed seven birdies and three bogeys with an eagle at the long 11th, while Lowry looked to be surging into a clear lead when he holed a six footer for birdie at the 15th and gained another shot from ten feet at the 16th.
However, he failed to get up and down from a greenside bunker at the 17th and paid the price for driving into sand at the last - the two closing bogeys souring the Irishman's round somewhat.