Green ended up with a 1-under 71, as did Goosen, as the pair were the overnight co-leaders. O'Hern posted a 3-under 69 to join the second-round leaders at 12-under-par 204.
Defending champion Henrik Stenson put himself in position to repeat after a third-round, 2-under 70. Edward Michaels shot a 3-under 69 to join Stenson in a tie for fourth place at 10-under-par 206.
Green stood on the 18th tee with a two-shot lead, but drove into rocks and was forced to take a penalty drop. He got on the par-5 green in four, but three-putted for a disastrous double-bogey seven.
That horrible miscue tarnished an otherwise strong day for the left-handed Australian. Green was 2 under par through seven holes, then parred his next seven holes around the turn.
He birdied the par-4 15th, which gave him a three-shot cushion over O'Hern. Green parred 16 and 17, as the others picked up one shot, but his meltdown at 18 cost him a decent-sized advantage with one round to play.
'I played pretty nicely from the word go,' said Green, whose only tour victory came at the 1997 Dubai Desert Classic. 'Gathered a nice bit of momentum and played pretty nicely, but it was just a bit of a shame about the last hole.'
Goosen trailed early thanks to both Green's strong play, and an even-par opening nine. The No. 8 player in the world parred his first three holes on the second nine, but trouble loomed.
He bogeyed the 13th and 14th holes and found himself four behind Green. Both players birdied 15, but Goosen polished three birdies in a row thanks to a three and a two at 16 and 17.
Despite not playing a particularly good round on Saturday, Goosen just felt happy to still hold a spot atop the leaderboard when the final putt went in the hole.
'I needed to finish with three birdies in the last four holes to have any sort of a chance,' acknowledged Goosen, a 13-time winner on the European Tour. 'I didn't quite expect to be sharing the lead. I was expecting to maybe be two behind. Unfortunately Green hit in the rocks on the 18th and made double. It was tough out there today.'
O'Hern, like Green, a left-handed Australian, flew out of the gate with a pair of birdies. Unfortunately, he dropped shots on his next two holes and parred out for a 36.
He crept up the leaderboard with a great back nine. He birdied the 10th for the second consecutive day, then recorded birdies at 14 and 16 to find himself tied for first.
O'Hern has yet to visit the winner's circle on the European Tour, but did win the Australian PGA Championship last month on the Australasian Tour to bring positive memories into the final round.
'I feel pretty good about it because I won two tournaments ago,' said O'Hern. 'So I'm feeling good going into tomorrow plus I'm playing well. You can't ask for more to be going into Sunday with the lead and playing well. If you can do that, you've got a real good chance.'
Paul Lawrie, the 1999 British Open champion, managed a 1-under 71 on Saturday and is tied for sixth place with Soren Kjeldsen (66) and Peter O'Malley (67) at minus-9.
Three-time major winner Ernie Els carded a 4-under 68 and shares ninth place with Wen-Chong Liang (72) and Andres Romero (67). The trio is knotted at 8-under-par 208.
The Golf Channel will have coverage of all four rounds beginning at 9:30 a.m. ET each day.