Goosen holed a gutty six-foot par putt at the par-5 18th of the Gary Player Country Club after dumping his second into water behind the green.
'I'm very tired,' said Goosen, who matched Drummond with a 69 on Friday. 'I couldn't sleep and it caught up with me.'
Goosen looked to be in command with a three-shot lead heading into the back nine but a birdie by Drummond at the par-5 11th cut the lead to two. It was two back-nine par-3s that brought the Scotsman even with Goosen.
The reigning U.S. Open champion bogeyed No. 13 and that left him one shot ahead of Drummond but that lead turned into a deficit after Drummond birdied the 14th and 15th to reach 15-under par.
Goosen dropped another shot at the par-3 16th to fall down by two but Drummond took his turn losing a stroke, bogeying No. 17. Goosen was able to collect birdie at the same hole to draw even before the duo both parred the closing hole.
'I was excited at playing with Retief, but I was a bit shaky over the first four or five holes as a result of it,' said Drummond, who holed a 40-yard chip-in for eagle at No. 5. 'I hit quite a few poor iron shots on some of the shorter par-4s, which I should've been able to birdie.'
Jaco Van Zyl, a South African, fired the lowest round of the day with an 8-under 64 on Saturday and drew to within two at 12-under.
David Park and Craig Lile share fourth at 10-under 206, followed by Paddy Gribben, Desvonde Botes and Tjaart van der Walt, who share fifth at 9-under.
Nick Price posted a 5-under 67 on Saturday and is in a logjam in ninth at 8-under par.
Defending champion Darren Clarke put together his second consecutive 68 to reach 7-under, seven shots out of the lead.