Making his fifth US PGA Tour start, Huh parred all eight holes in the play-off that matched the second-longest in history.
The 21 year old Huh closed with an eight under 65 to match Allenby at 13 under on the seaside El Camaleon course.
Allenby had a two stroke lead with a hole to play in regulation, but the 40 year old Australian closed with a double bogey.
The play-off fell three holes short of the 11 set in the 1949 Motor City Open when Cary Middlecoff and Lloyd Mangrum were declared co-winners.
Spain’s Alejandro Cañizares finished in a tie for fifth on ten under, along with overnight leader Daniel Summerhays.
