'I didn't know if I was ever going to win again,' said Fiori, who collected $300,000 for the victory. 'It was nice to get into contention and compete.'
Fiori began the day seven shots off the pace but fired a 67 to match overnight leader Graham Marsh in the clubhouse at 6-under-par 210.
The duo went back to the par-5 18th at BosqueReal Country Club to begin the playoff and both players struggled early in the extra session. Fiori scrambled to the green and chipped his fourth inside 25 feet. He ran his putt within a foot of the hole and tapped in for a bogey.
Marsh found a hazard with his approach to the green at 18 and was left with an eight-foot putt for a bogey to extend the extra session. The Australian drained the putt and the pair were off to the par-4 16th.
Marsh opened the door for his competitor after his tee shot found the left rough.
Fiori welcomed the advantage and knocked his second shot to the fringe. Marsh left his approach short of the green but answered with a perfect chip that stopped within a foot of the hole. Fiori also played his third to tap-in distance and each player walked away with par.
Marsh's second shot came up short again at the third playoff hole, the par-4 17th. Fiori then dropped his approach within 20 feet of the hole and took two putts for par and the win.
Fiori jumped out of the gate with a birdie at the opening hole. He then ran off four consecutive birdies starting at the par-4 third to move to minus-6.
He stumbled to a bogey at the 16th but managed a birdie at the par-5 last to force the extra session.
Marsh was in control throughout the final round and birdied three in a row from the 10th to open a three-shot lead at 9 under par.
The 60-year-old faltered on the way in, however, with three bogeys over his last six holes to fall back into a tie with Fiori after a final-round 74.
Hugh Baiocchi finished alone in third place at 5-under-par 211. Jay Sigel, Jim Ahern and Jack Spradlin followed at 3-under-par 213.
Andy Bean, who held the lead after the first round, joined Hale Irwin, Sam Torrance and Tom Jenkins in a tie for seventh place at 2-under-par 214.