Oosthuizen, the 2010 British Open winner, missed the 54-hole tournament record by a single stroke en route to the lead, and was especially tough on the back nine, where he recorded four birdies over five holes.
The South African is seeking his second career PGA Tour victory -- he has four titles on the European Tour.
Grabbing second place at minus-15 was Hunter Mahan, who carded a 7-under 65 on the Tournament Course at Redstone Golf Club.
James Driscoll (71) finished Saturday two strokes back at minus-12, while defending champion Phil Mickelson carded a 2-under 70 to share sixth place with Ryan Palmer (66) and Keegan Bradley (69) at 11-under 205.
Swim Week Miami Beach 2014 [PHOTOS]