The South African, who had made the cut only once in his first eight major championships, took a four-stroke lead into the final round Sunday at the Old Course.
Oosthuizen posted three straight rounds in the 60s, including a 3-under 69 Saturday that gave the rest of the field plenty of work to do trying to chase down his 15-under 201.
Paul Casey was the closest challenger at 205, the best hope to end Britain's 11-year winless streak in its home championship. Germany's Martin Kaymer (208) was the only other golfer within seven strokes.
While an Oosthuizen victory would be a huge surprise, it wouldn't be unprecedented for someone to emerge from obscurity at golf's oldest major. Ben Curtis was ranked 396th in the world when he won at Royal St. George in 2003. Todd Hamilton stunned Ernie Els in a playoff at Troon the following year.
If nothing else, someone looks likely to win their first major championship at St. Andrews. Among the top 17, only two-time U.S. Open champion Retief Goosen (211) had one of golf's biggest titles on his resume.
The final round started in warm, calm conditions, giving the early starters a chance to put up some low numbers. Wearing a gaudy orange outfit, Rickie Fowler of the U.S. birdied the last two holes for a 67. Alvaro Quiros also had a 67, while Trevor Immelman of South Africa and Edoardo Molinari of Italy shot a pair of 68s.
But the wind was expected to pick up in the afternoon, making it tougher on those at the top of the leaderboard.
Tiger Woods' hopes of winning a third straight Open title at St. Andrews were likely snuffed out when he shot a second straight 73 on Saturday. The greens have been his main problem _ he needed a staggering 35 putts to get through the third round _ so he switched his short stick for the second time this week.
Woods had changed to a Nike Method putter during the practice rounds, believing it would help him cope with the slower speed of St. Andrews' massive greens. But he took 99 putts through the first three rounds _ 11 more than Oosthuizen _ so he went back to the Scotty Cameron putter made by Titleist, the model he has used since 1999.
Facing a 12-shot deficit heading into Sunday, Woods got off to a promising start with birdies on two of the first three holes. But a double-bogey at No. 4 left him right where he started.
No one has ever come back from more than a 10-shot deficit on the final day to win a major championship.