Fasth had fallen out of the lead in the third round with a 75 at Gulf Harbour Country Club, but the Swede stormed back on Sunday with a 63, his second of the tournament, to reach the clubhouse at 22 under.
Miles Tunnicliff then made one final push with a birdie at the par-4 18th to force the extra session where Fasth ultimately prevailed.
Australians Richard Green and Simon Nash shared third place at 18-under-par 270. Fellow Aussie Peter O'Malley was one shot further back along with Sweden's Robert Karlsson at 17-under-par 271.
Fasth took the lead heading into the weekend with a 63, but was passed on the leaderboard after a disappointing Saturday. With that poor round behind him, the former Ryder Cup player set out to redeem himself in the final round.
The 32-year-old tallied his first birdie of the day at the par-5 second and picked up another birdie at the par-4 fifth. Fasth then eagled the par-5 sixth and added a birdie at the par-4 seventh to move to 18 under.
Fasth kept on rolling with back-to-back birdies from the 10th and a birdie at the 13th to stand atop the leaderboard. After Tunnicliff holed out for an eagle at the par-4 12th to grab a share of first, Fasth birdied the 17th to regain the outright lead.
Tunnicliff then birdied the closing hole before falling short in the extra session.
After both players parred the first playoff hole, Fasth played his approach inside 15 feet at the par-4 18th and sank the putt for the winning birdie.
Tour rookie Oliver Wilson held the lead heading into the final round, but the Englishman struggled out of the gate on Sunday. He dropped his first shot with a bogey at the second but was able to recover with a birdie at the sixth.
Wilson then bogeyed the ninth to fall further off the pace and he continued to sink with bogeys at the 14th and the 16th. The 24-year-old salvaged what he could with a birdie at the 18th to complete a round of 74.
Wilson was joined by Jarrod Moseley, Rolf Muntz, Jose Manuel Lara, Damien McGrane and Steve Alker in a tie for seventh at 15-under-par 273.
'I hardly missed a green and had birdie chances I missed on both the front and back nines,' said Alker, who finished as the top New Zealander. 'I've been struggling a little bit with my putting and the greens are so good here that you feel you've given a shot away if you miss from 10 to 15 feet'