Fernandez-Castano collected his second European Tour victory as he titled at last year's KLM Open.
Stenson, who held the lead after the first three rounds, had no one to blame for second place but himself. He was three ahead after eight holes, but a triple-bogey at the ninth made the race to the winner's circle wide open.
He birdied the 72nd hole for a 1-under 71. Stenson and Fernandez-Castano finished regulation knotted at 7-under-par 281.
At the first playoff hole, Fernandez-Castano left little to the imagination about who would have their name engraved on the trophy. He knocked his approach to tap-in range, then kicked it in to earn his first playoff victory on the European Tour.
'I'm glad I knocked it to just four inches,' said Fernandez-Castano. 'Otherwise I would have missed it, I was so nervous.'
Eight-time Order of Merit champion Colin Montgomerie and Jose-Filipe Lima both fired matching rounds of 4-under 68 to share third place at 6-under-par 282.
Paul Casey (71), Simon Dyson (68) and Mahal Pearce (71) tied for fifth place at minus-5.
Stenson took control of the tournament thanks to three straight birdies from the sixth hole. The 15th-ranked player in the world reached 9-under par and owned a three-shot cushion, but disaster struck.
Stenson triple-bogeyed the par-5 ninth hole to fall into a six-player tie for the lead. Lima moved into sole possession of first place thanks to an eagle at the 13th, but that was short-lived as he bogeyed the next hole.
The next player to assume the top spot on the leaderboard was Pearce. He birdied the 12th, but like Lima, bogeyed his next hole and once again six golfers were knotted in first.
Stenson reclaimed the lead with a birdie at No. 14, but that did not last long. He bogeyed the 16th hole to move back to 6 under, but Fernandez-Castano was there to assume the lead.
Fernandez-Castano played solid golf throughout the day with 13 consecutive pars to open his round. He birdied No. 14 to reach 6-under par and when his playing partner, Stenson bogeyed 16, the Spaniard birdied the same hole to get first place.
Fernandez-Castano chipped in from off the green for his birdie and ended up parring out. He had to wait to see if his closest competitors could catch him.
Montgomerie and Lima got into the clubhouse at 6-under par, meaning only Stenson had a chance to match Fernandez-Castano in the lead. Stenson did just that with a birdie on the 72nd hole, but was not able to handle the Spaniard in the extra session.
'It's a dream come true,' admitted Fernandez-Castano, who finished as runner- up last week at the China Open. 'Winning the BMW Asian Open is a great thing. It's unbelievable!'
Peter O'Malley (73), David Bransdon (66), Terry Pilkadaris (65) and 1999 British Open champion Paul Lawrie (71) finished in a tie for eighth place at 3-under-par 285.