A birdie at the 3rd hole from 12 feet saw Leishman move ahead in the match but Oostuizen immediately responded with birdies at the 4th and 5th.
Leishman squared the match at the with a birdie at the 6th but soon after Oosthuizen took control of the match by taking a three-hole lead through 10 holes.
Leishman reduced the margin with birdie at the 14th but he was unable to gain any further ground and the pair shook hands at the 17th.
Oosthuizen, though, would go on the lose to American Kevin Kisner in the afternoon quarter finals.
The match that would steal most attention on Saturday morning, however, would be the gripping encounter between Tiger Woods and Rory McIlroy.
After a series of pars over the opening four holes Woods edged ahead when he birdied the drivable par 4 5th hole after his tee host finished just short of the green.
Woods birdied the next and when he added another birdie at the 10th he had moved 3 ahead and the match appeared to be all but over.
McIlroy, however, saw it differently and fought back birdies at the 12th and 13th and there was just one hole between arguably the game’s two most exciting players.
The straw that would finally break McIlroy’s back would come at the 16th when, appearing to have the ascendancy after a superb drive, McIlroy finished just short of the green side bunker with his approach at the par five and then almost inexplicably floundered his way before conceding the hole.
That saw Woods 2 ahead with two to play and when Woods saved par from short of the green at the 17th it was all over.
The volatility of 18 hole match play encounters was no better displayed than in Woods' afternoon match against Lucas Bjerregaard the 50th ranked player in the field. Any player in this field is capable of beating another on any given day and so it would prove.
The match see-sawed throughout both players ahead at various stages although three was never more than 2 holes between the pair. Bjerregaard squared the match with a brilliant eagle at the 16th and when both players hit stunning tee shots at the 17th and converted for birdies they headed to the 18th hole all square.
When many felt it would be Bjerregaard who would succumb at the final hurdle it was Woods who surprisingly pitched into the bunker from just short of the green and failed to get up and down to hand the match to the ever-improving Danish golfer.
Understandably Bjerregaard was excited about what he had achieved.
“It's up there with my best days, that's for sure," he said. "We had a great match, it's a shame it had to end like this. It really didn't deserve that. Obviously I'm happy to come out on the winning side. But we had a great match and I really, really enjoyed playing with him today.
“I've never played with him before, so it was a cool experience for me and obviously to say I've beaten Tiger, there's not a lot of guys that can say that, so it's up there. It's so different to what I've ever experienced before.
“And I've played with some good golfers before, but I've never heard so many yell his name and all the stuff all the way around. And it was really cool to experience. And I actually thought it was really enjoyable. But it must be hard, as well, doing that every day.
“The support out there was great. A lot of people yelling my name as well, and having a bit of fun with it. So there was support for me as well.”
In tomorrow's semi-finals Bjerregaard takes on 2013 champion, Matt Kuchar, and Francesco Molinari faces Kevin Kisner
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