Fleetwood had three other birdies in addition to the one on 18 against one bogey on the day for a 3-under-par 69. He's at 10-under 206 after 54 holes.
Joost Luiten missed an eagle try at the 18th -- a par-4, 273-yard hole -- and settled for birdie that put him at 9-under for the tournament after a third-round of 2-under 70. He's tied with Victor Dubuisson, who on Saturday turned in a third consecutive 69, for second.
Defending champion Louis Oosthuizen, who was tied with a Fleetwood and Luiten for the 36-hole lead, had a triple-bogey 7 at the 16th and three bogeys Saturday in a 1-under 71 for the round. He's in fourth place at 8-under.
Branden Grace started Saturday with back-to-back bogeys but, fueled by a third-hole eagle, was 4-under on the day to move into fifth place at 7-under.
Fleetwood had birdies at the third and fourth holes Saturday and was still even with Oosthuizen for the lead until Oosthuizen had bogeys at Nos. 6 and 7.
He kept ahead with a birdie at No. 9 and his only slip of the day came at 14 where he three-putted from the fringe for a bogey 6. The birdie at 18 kept him ahead.
Swim Week Miami Beach 2014 [PHOTOS]