McIlroy fired a closing four-under-par 67 on Monday to triumph at 20-under 264, one shot clear of Oosthuizen (71) and two ahead of Woods (66), claiming his third win of the year.
It was his second victory in three starts, having won the US PGA Championship by a record eight shots last month.
Phil Mickelson (66) and fellow American and Ryder Cup hopeful Dustin Johnson (70) tied for fourth at 14-under-par.
Some late McIlroy stumbles gave Oosthuizen a 12-foot putt on the last to force a playoff but it wouldn't drop.
"I didn't finish it off the way I would have liked but I got there in the end so I'm very happy," McIlroy said.
"It's my third victory of the year and great to get a victory in the playoffs.
"It sets me up in a great position going into the next two weeks."
Adam Scott made a final round charge to be the leading Australian, carding a 66 to tie for seventh, eight shots behind McIlroy.
Scott's finish remained significant though as it moved his standing in the FedEx Cup inside the top 30 to 25th.
The top 70 in the season-long points race advance to Crooked Stick in Indiana later this week before the top 30 move on to the Tour Championship in Atlanta for a shot at not only a prestigious win, but also the FedEx Cup for the points winner and the $US10 million ($A9.75 million) bonus that goes with it.
"I had the weekend I wanted," Scott said.
"I salvaged something out of this week after a frustrating first two days.
"I felt like I played well enough to win yet I'm 10 shots back because I just didn't putt well."
John Senden produced another solid week, finishing 12th at nine-under although he cost himself a top 10 finish when he four-putted the final green from just seven feet.
He'll also move to Indiana inside the top 30 in points at 26th.
Greg Chalmers (-3), Aaron Baddeley (-2), Marc Leishman (-2), Jason Day (Even) and Geoff Ogilvy (Even) were well off the pace.
Chalmers, Leishman and Ogilvy survived to next week while for Baddeley and Day it is the end of the playoffs road.
McIlroy started the final round three back of Oosthuizen but made three consecutive birdies from the second to the fourth hole to pull within a shot.
Both McIlroy and Oosthuizen found trouble off the tee on the fifth, the former in a bunker and the latter in the woods.
McIlroy ended up with a bogey but still joined the lead after Oosthuizen carded a double bogey and then took top spot outright with a precision approach and tap in birdie on the sixth.
He led by three after a birdie on the 12th before the South African birdied the 13th and 15th to pull within a stroke.
Both bogeyed the 17th and McIlroy opened the door again when he drove into trouble on the par five last but Oosthuizen's approach sailed into the deep rough.
He flopped the ball to 12 feet and after McIlroy's 20-foot birdie putt stopped on the edge he had a chance to force a playoff but slid the ball past the cup.
