O'Hara, who failed to break 70 in the first two rounds, notched seven birdies and no bogeys in the round to take a two-shot lead over Gaganjeet Bhullar, Gary Boyd and second-round leader Mikael Lundberg.
Fisher had a more up-and-down round that included an eagle on the 11th hole en route to a 68.
Several players had to complete their second rounds on Saturday before teeing up for the third. A thunderstorm Friday short-circuited play, but the weather was more hospitable Saturday.
Swim Week Miami Beach 2014 [PHOTOS]