Beljan fired a three-under par 69 to finish at 16-under-par for the season-ending tournament, besting fellow Americans Robert Garrigus (68) and Matt Every (68) who tied for second at 14-under while Brian Gay (70) was a shot further back in fourth.
Suffering heart palpitations and shortness of breath during the second round, the 28-year-old spent Friday night in hospital but still managed to enter the final round with a two-stroke lead.
"This is the greatest feeling ever. I'm speechless. It's wonderful," Beljan told reporters after his first PGA Tour win.
"My family flew in last night and I have everybody back home rooting for me. I didn't even think I was going to get to finish my round on Friday.
"Yesterday I showed up just trying to be able to finish 18 holes and now here I am the Children's Miracle Network Hospitals Classic champion. What a joy."
Starting the week at 139th on the money list and facing the prospect of losing his tour card for 2013, Beljan traded two bogeys with two birdies over the first five holes, leading many to believe his symptoms would eventually get the better of him.
But in a stunning turn of events he rammed home five birdies in a six-hole run between the seventh and 12th holes to put a gap on the field and lead by as many as five.
"I did not feel well this morning," Beljan revealed. "Not the same symptoms but my stomach was hurting, my head was pounding and I thought 'Here we go again.'
"But you know what, it may have taken a lot of the other nerves off that I may have felt if I was thinking about the golf."
A nervous double bogey after tree and sand trouble on the 13th was just a temporary stumble as another birdie on the 14th allowed Beljan to regain control of his round and although he bogeyed the final hole he still did more than enough to claim the win.
"I came here just trying to play well with not even the top 125 on my mind but now, golly, what a great deal," Beljan said. "It's been a tough year but a great year to top it off like this."
Beljan became the fourth rookie to win on the 2012 US PGA Tour, following John Huh (Mayakoba Golf Classic), Ted Potter Jr. (Greenbrier Classic) and Jonas Blixt (Frys.com Open).
Tim Herron was the only other golfer to pull into the top 125 on the US PGA Tour's season-ending money list to secure full playing privileges for next year. His tie for ninth was enough to leap him 12 shots up the list to 124th.
American Jerry Kelly, despite also finishing in a tie for ninth, finished just a spot behind the 125 mark while Australian Rod Pampling and American Billy Mayfair both fell from inside the top 125 to outside after missing the cut on Friday.
Other big names to finish without cards include Camilo Villegas, John Daly, Stuart Appleby and two-time heart transplant recipient Erik Compton.
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