The Spaniard finished at 10-under 203 after 54 holes, two better than former co-leader Nick Watney.
The performance continued a recent streak of fine play for Garcia, who won the Wyndham Championship Monday -- garnering himself a berth on the European Ryder Cup team -- and is also in contention for the FedExCup title.
Watney bogeyed the final hole for an even-par 71, ending at minus-8, while Kevin Stadler fired a 6-under 65 to jump 39 places to third at minus-7.
Tiger Woods, who suffered from a sore back Friday, struggled with his putter in Round 3 and could manage only a 1-over 72, good for a 10th-place tie at 4-under 209.
Swim Week Miami Beach 2014 [PHOTOS]