The performance put Levin at 8-under 208 after 54 holes -- the second time this year he's entered the final round with an advantage.
Levin led by six strokes at Phoenix Open in February but ended up finishing third.
Rory Sabbatini, who led after two rounds, fell into second place with a 1-under 71, one shot back at minus-7.
Making a big gain Saturday was Rickie Fowler, who fired a 3-under 69 to grab sole possession of third at 5-under 211.
Tiger Woods, who came into the day tied for second, carded a 1-over 73 to fall into fourth place at minus-4.
Swim Week Miami Beach 2014 [PHOTOS]