Grace had an eagle at the par-5, 593-yard sixth hole and one bogey against seven birdies in the third round. He's at 18-under 198 after 54 holes.
Defending champion Nicolas Colsaerts had a bogey-free 6-under 66 Saturday for a three-round total of 15-under while Fabrizio Zanotti, who opened and closed with back-to-back birdies, shot 64 Saturday and moved into third, four strokes back of Grace.
Five players, including second-round co-leader Jean-Baptiste Gonnet, are tied at 13-under with three others, including Gary Boyd, the other second-round co-leader, are 12-under.
Grace chipped within 1 foot for an easy birdie putt at the second hole and dropped a putt from the fringe at No. 5 for another. A 20-foot putt at 6 was worth an eagle 3. Another short putt at the seventh hole gave him the lead.
He had a birdie at 11 but three-putted 14 for a bogey. But sharp iron play set him up for short birdie putts on 15, 17 and 18 for the 64.
Swim Week Miami Beach 2014 [PHOTOS]