They were at nine-under 135, two strokes ahead of American J.B. Holmes on a day when the top four on the leaderboard played in the more amenable afternoon conditions.
Many of the big names have work to do, defending champion Jason Day trailing by seven shots, with Dustin Johnson, Sergio Garcia and Rory McIlroy nine behind.
“I’ve been playing well for a while now,” Oosthuizen told reporters, happy to reap reward for his recent focus on putting.
“I've been probably working a little bit more on my putting at home ... and I think it's paid off.
“I'm rolling the ball really nicely and feel really confident on the greens.”
Apart from winning the 2010 British Open by seven strokes at the home of golf, St. Andrews, Oosthuizen lost two majors in the playoffs, the 2015 British Open, which was also at St. Andrews, and the 2012 U.S. Masters.
Stanley notched his lone PGA Tour victory in Phoenix in 2012. He has not quite kicked on as many expected, but has been quietly working his way back into form.
“My putting has been a little bit inconsistent, but from a ball-striking standpoint, I'm not really sure I can ask much more out of what I've been doing this year,” said Stanley, whose putting this week has benefited from a posture adjustment.
Lurking close was 54-year-old Singh, who despite a few strands of grey hair is not out of place against men half his age.
"I haven't won in donkey's years (but) I think I still can compete out here, and as long as I think I can compete, I'll play here,” said the Fiji-born winner of three major championships, who lives near the course and is a constant presence at the driving range.
Singh, who temporarily supplanted Tiger Woods atop the world rankings in 2005, has not triumphed on the PGA Tour since 2008, but hope springs eternal.
“If you think you’re coming out here just to make the numbers, you’d better stay home,” he said after bogeying the last for a 68.
(Reporting by Andrew Both in Cary, North Carolina, editing by Ed Osmond / Ian Ransom)
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