With his total of 16-under-par 194 through three rounds, the Swede bettered the tournament's 54-hole total by one stroke.
"I am very happy with the way I played today and that is the most important thing," he said. "You'd take a four shot lead on any course but this is definitely a tricky course to try and pick up a lot of shots on (and) my focus is on another good solid round (Sunday)."
Spain's Miguel Angel Jimenez stayed in second place after a matching 4-under 66. His total is 12-under 198.
Three others, including former Masters champion Mike Weir (67), are tied for seventh at 10-under 200.
Swim Week Miami Beach 2014 [PHOTOS]