Huh, a PGA Tour rookie, carded an 8-under-par 63 in the final round, while Allenby blew a chance to win the event in regulation when he stumbled to a double-bogey on the par-four 18th to close out the round with a 6-under 65.
Both golfers finished at 13-under-par 271, then embarked on their marathon playoff at El Camaleon Golf Course.
Each matched pars over the first seven holes before Allenby faltered on the eighth with a bogey. Huh posted yet another par to claim his first PGA Tour title.
Sharing third place were Matt Every and Colt Knost, each of whom fired 5-under 66s to finish at minus-11.
Chris Stroud (71) finished in a four-way tie for third place one shot further back after missing a chance to make it a three-way playoff with a double-bogey on the final regulation hole.