Sweden's Henrik Stenson fired the best round of the day with an 8-under 64 to join Goosen at 15-under-par 201. Nick Dougherty (66) and co-overnight leader Anthony Wall (68), both of England, are also at minus-15.
The leaders stand one stroke clear of Briton David Lynn, who shot a 67 to hold fifth place at minus-14. Spain's Jose Maria Olazabal, who shared the overnight lead with Wall, is one stroke further back in sixth place after a 70.
Goosen held the outright lead at 16 under after an eagle at the par-5 13th, where he rolled in a 25-foot putt, and a birdie at the 15th, his fifth of the round.
But the two-time U.S. Open winner dropped his first stroke of the day with a bogey at par-3 16th, where he hooked his tee shot left of the green. That dropped him into a tie with Stenson and Dougherty, who were already in the clubhouse at minus-15. Otherwise, the South African would hold the lead.
'I am delighted to be in this position because, to be honest, I haven't really done well here in the past,' admitted Goosen. 'But it is going very well for me this week so far, and if the weather stays like this tomorrow, then I am going to need another low round to win.'
The 29-year-old Stenson collected eight birdies in his bogey-free round, including five on the back nine to move from a tie for 10th place into a share of the lead. With a pair of second-place finishes already this season, the two-time European Tour winner will be seeking his first title since The Heritage last year.
'I think tomorrow I just have to give it a hundred percent and play aggressive and make some birdie putts, because there is going to be someone coming out and making a charge when it is this bunched up,' said Stenson.
'Birdies are the only thing which matter, really. You just want to go out and shoot another low score and hope it is good enough.'
Dougherty, who entered Saturday tied for fourth place with Goosen and two others, is seeking his second career title on tour after collecting his maiden victory at the Caltex Masters in January.
The 23-year-old stumbled to a double bogey at the par-5 seventh, which put him at even par through the front nine. But he made up for that mistake by scorching the inward nine with four birdies and an eagle at the 13th.
'I'm very pleased with what I did out there today,' said Dougherty. 'I made more of my fair share of birdies on the back nine today...Hopefully there are more birdies out there waiting for me tomorrow.'
Wall dropped a shot at No. 1 after shooting a bogey-free 62 in the second round. He stumbled to three bogeys on the front nine, actually, and made the turn at minus-11.
But the 30-year-old ended his round by playing the final six holes at 4 under. Like Goosen and Dougherty, his back nine included an eagle at the par-5 13th, and he joined the leaders with a birdie at 18.
'I know I'm going to need another low round, but there is no reason why I shouldn't score one,' said Wall, whose lone European Tour victory came at the 2000 Alfred Dunhill Championship.
'I am looking forward to it,' he added. 'It is a great challenge and a great test for me. It is nice to be back in the mix again...nice to still know that I can do it.'
England's David Howell fired a 6-under 66 to move into a tie for seventh place with Thomas Levet (67) of France and Scott Drummond (68) of Scotland. The trio stands at 12-under-par 204, one stroke ahead of six players tied for 10th place.