The 2010 Open champion went to number four for the first time by winning in South Africa, the third year in a row he has started with a victory.
Oosthuizen's closing 66 brought him from five behind Scotland's Scott Jamieson to one ahead, Jamieson being left to rue a double bogey on the fifth hole and a chip on the last that stopped two inches from the cup.
McIlroy is out on his own at present and will stay there even if he misses the halfway cut in Abu Dhabi this week and Woods wins.
"The top spot is a tough one, I think, at the moment," Oosthuizen said.
"But I'll try to make it to number two and then I guess I'll try to get to number one.
"Obviously Rory's in a great spot and he's swinging it well. Even if I or Tiger or Luke plays really well, Rory is still playing well.
"The difference will be the majors because they've got the big points. If I can get one this year - or two, even - it's all going to come down to them."
The first of the season is the Masters and it was at Augusta last April that Oosthuizen made an albatross on the second hole of his last round before losing a play-off to Bubba Watson.
Jamieson used to be a student at Augusta State University and might yet be back this spring.
The 29-year-old has finished first, third and second in the opening three events of the European Tour season, and has climbed in the rankings almost 100 places from the 168th place he held little over a month ago.
Jamieson needs to be in the world's top 50 at the end of March to earn a Masters debut.
Shane Lowry is also heading towards the world's top 50 as he finished in a tie for ninth.