He received a free drop, but was unable to get up and down for par.
Oosthuizen, who began the day five behind Garcia, made the quick start he needed with three birdies in the first four holes.
As Kim's challenge faded, three players pushed themselves into contention, J.J. Spaun and Brice Garnett joining Lee on the charge.
"I wouldn't say it was a frustrating back nine‚" said a pragmatic Garcia.
"It was very hard this morning, the wind was blowing a lot and the first few holes were straight into it".
"I'm going to see if I can shoot below 70 and see if that's good enough". "I probably shot the highest I could shoot today. I would have taken it if you offered it to me on Thursday morning".
McIlroy's front nine was promising with three birdies offset by just a single bogey, at the par-four third when his ball plugged just below the lip of a greenside bunker. But yeah, it was a tough day. For me it was just more of the same and shooting under par here is always great. I hung in there nicely.
Garcia, who is bidding to follow up his victory in the Andalucia Valderrama Masters last month, started the third round with a one-shot cushion and doubled that thanks to some solid iron play, although it could have been better for the Spaniard as he twice led by four shots.
An emotional Lopez beat off world number one Ariya Jutanugarn of Thailand and a late challenge from France's Celine Boutier for her maiden victory on the US-based LPGA Tour.
In contrast, Paul Dunne struggled to a six-over 78 as McIlroy got little reward for a moment of honesty at the 14th as he carded an ultimately disappointing level-par 72. His round was highlighted by holing a lengthy putt on 17.
"My grandpa passed away a couple of weeks ago".
"If I can tidy that up tomorrow I should be alright, but obviously I'm pretty disappointed right now", said McIlroy.
"Sadly I didn't, but he was with me all week long and I couldn't be more lucky, more fortunate, to have him still alive in me".
There was a tie for fourth between Danielle Kang of the United States and South Korea's Kim Sei-young.