Europe's Challenge Tour is the equivalent of the Nationwide Tour in the United States.
Floren, also seeking his maiden Challenge Tour title, had earlier set the clubhouse lead at Carya Golf Club in Belek, Turkey, after notching no fewer than nine birdies in a scintillating round of 63.
And when Ford, one shot behind, found trouble off the 17th tee, the title appeared to be heading the talented Swede's way.
But the Englishman had other ideas, pulling off a sensational recovery shot that curved around the trees and rolled to within five feet of the flag to set up a birdie, which saw him join Floren at the top of the leaderboard.
"My shot to the 17th hole was probably the turning point," said Ford, who lettered for the Vols from 2005-08. "I was on a down slope in the rough, so the ball was under my feet, and then I had a tree blocking my shot to the green. So to make birdie from there was a massive bonus – I could probably hit another 100 balls and not put it as close again."
He was unable to finish the job off in regulation play, as his birdie attempt on the 18th green shaved the cup. But after hitting his approach to 10 feet on the first extra hole, Ford made no mistake the second time around to receive the customary dousing of champagne from friends who had flown over to watch him play.
"On the 18th green I thought my birdie putt was in," he said. "It was tracking all the way and the crowd got a bit excited, but it just fell away at the last minute. But my putt in the playoff was on exactly the same line, just much closer in, so I would've been pretty annoyed with myself had I missed that. It was still a great feeling when it dropped in though. The first thing my caddy said to me was that he's going to retire with a 100 percent record, because this is the first time he's been on my bag!"
The win moved Ford, playing in only his fifth tournament since turning professional before the 2009 Qualifying School – Final Stage, to second place in the rankings behind his compatriot Robert Dinwiddie.
"Even in my wildest dreams, I hadn't expected to win so soon in my professional career," Ford said. "I was a little bit nervous for the first few holes, which I thought I would be, but after that I started to play well and settled into a rhythm.
"The only poor shot I hit all day was my drive on the ninth hole, where I've struggled all week. But apart from that, I didn't look like dropping a shot all day."
Floren could console himself with a check for more than $25,000 that moved him up five places to fourth in the rankings, while England's Stuart Davis – whose birdie putt on the 18th green drifted agonizingly past the cup – took third place, one shot back on 10 under par.
South African Branden Grace and Norway's Jan-Are Larsen both posted rounds of 69 to share fourth place on 9 under par.