Oosthuizen made a 20-foot birdie putt on the 18th hole to finish his round with 5-under 67 and a total of 10-under 134.
The South African led France's Francois Delamontagne (66), first-round leader Matthew Zions of Australia (70) and Italian Open winner Gonzalo Fernandez-Castano of Spain (68).
Steve Jones, the 1996 U.S. Open winner, is at 8-under 136, along with Westwood.
Jones saw a bogey at No. 18 spoil his round of 67, which included an eagle 2 at the 15th. He was 60th at last week's Italian Open, and played this round with Westwood.
'You can feed off each other and it was nice to see him really bombing it,' Jones said. 'He's going to be the one to catch the way he is playing.'
Westwood changed putters and had a bogey-free round. The Englishman moved into contention for his first European win in four years.
'I used it in the first round of the Masters and swore I'd never use it again, but it seems to roll the ball well on these greens and anything would have been better than yesterday,' said Westwood, who shot a 72 in the first round.
'My long game has been pretty good all year and I just haven't been able to match it up with a decent putting round, so it was nice to get it right today,' he said.
David Higgins of Ireland (68), Sweden's Michael Jonzon (68), Richard McEvoy of England (68) and Spain's Carl Suneson (68) were tied for fourth, three shots back of Oosthuizen.