The total gave Beljan a two-stroke win at 16-under-par 272 and allowed him to retain his tour card for the next two seasons.
The 28-year-old battled a health scare on Friday, when he was hospitalized overnight with shortness of breath and a rapid heart rate, but he returned Saturday and managed to retain the lead with a 71 at the Walt Disney World resort.
Beljan wrapped up the win Sunday, carding five birdies in a six-hole span from the 7th hole to pull away for the victory.
Sharing second place were Robert Garrigus and Matt Every, both of whom shot 4-under 68s to end at minus-14.
One stroke behind them was Brian Gay, who carded a final-round 70.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys