Goosen was two behind compatriot Ernie Els overnight, but with World Number 12 Els mixing three bogeys with three birdies on the front nine, Goosen was able to surge ahead as he reached 17 under.
He birdied the second and third, before compiling a hattrick of gains from the sixth.
Four-time winner of the event Els had been joined in second place by Open Championship winner Louis Oosthuizen, who was four under through ten holes.
England's Robert Rock moved into sole possession of fourth with a five under par 67 to lie 11 under.
The third and fourth rounds were both being played on Sunday after rain washed out much of Thursday, after organisers had cut the field to top 50 and ties following Saturday's second round.
Further morning rain caused a one hour delay in the morning and, with the fourth hole flooded, the decision was taken to reduce the course to 17 holes with all players given a nominal par.