Elson, a 29-year-old Briton, has only one career win in the European Challenge Tour to his credit. He finished 54 holes at 7-under 206, one stroke in front of second-round leader Robert Dinwiddie (even-par 71) and Raphael Jacquelin (66).
Dinwiddie got hot on the back nine, forging a first-place tie with Elston after tallying three birdies in a four-hole span, ending with the 16th. But the top money winner on this year's Challenge Tour missed a short par putt on 18 while Elston parred his final two to fall a stroke behind.
Mark F. Haastrup shot an even-par 71 to share fourth place with Martin Wiegele at minus-4.
Matt Haines (72) finished at 3-under 210, good for sixth place, while Joakim Backstrom (70) was one further back at minus-2.
Swim Week Miami Beach 2014 [PHOTOS]