Goosen, who lost in a playoff to Sergio Garcia last season, was able to handle more than the demanding conditions at The Gary Player Country Club Course all week.
He acknowledged that he considered withdrawing on Wednesday because his daughter Ella was admitted to a London hospital with bronchitis and he had not yet fully recovered from the flu that plagued him at last week's PGA Grand Slam of Golf.
'I was determined to play well and make it worth staying,' said Goosen. 'I haven't been feeling great the last three weeks, but the medics here have been outstanding and they've pumped me up with vitamin boosters. I started feeling better yesterday.'
Goosen came into the final round trailing Lee Westwood by a shot, but the South African quickly moved into first. He birdied two and six, then nearly holed his tee ball at the par-3 seventh to set up his third birdie of the round.
Goosen missed a birdie attempt at the eighth, but overcame the miscue at nine. He hit a long drive that left with an 8-iron into the par-5, island green. Goosen's approach stopped 3 feet from the hole and he tapped in the eagle putt to take a five-shot lead into the second nine.
A pair of loose drives cost Goosen bogeys at both the 10th and 11th holes, but the two-time U.S. Open champion rebounded. He drained a long birdie putt at 12, but failed to get up and down for par from the side of the green at 13.
Goosen was still five ahead as no player made a run at the top spot. He birdied 14, but bogeyed the last even though it would not matter. Goosen picked up the six-stroke win and cemented his status as the best player in bad conditions.
'I knew it would be a very tough day today as soon as I woke up and saw the wind blowing stronger than it has all week,' said Goosen. 'The course was one of the toughest I've played on all year, totally different to how it's ever been before. The greens are very firm and the landing areas so small. The course definitely showed its teeth.
'But I like it when it's really tough and you have to really grind it out.'
Els posted a 1-under 71 on Sunday while Appleby only managed a 2-over 74.
American Ryder Cuppers Jim Furyk (72) and Chris DiMarco (74) tied for fourth place at even-par 288.
Westwood struggled to a 7-over 43 on the second nine. He finished with an 8-over 80 on Sunday and tied for sixth place with 50-year-old Jay Haas at plus-3.
Reigning British Open champion Todd Hamilton shot a 3-over 75 and took eighth at 4-over-par 292. Nick Price carded a 6-over 78 in the final round and came in ninth at plus-5.
Fredrik Jacobson shot an even-par 72 and took 10th place at plus-9, followed by Chad Campbell, who also posted a 72, who took 11th at 11-over-par 299.
Garcia polished off the worst performance by a defending champion in tournament history. He managed a 6-over-par 78 and came in last at 15-over- par 303.