The trio finished regulation tied at 15-under-par 273 and headed to the par- five 18th hole at Golfclub Munchen Nord-Eichenried to begin the sudden-death playoff.
Goosen and Stenson both found the fairway off the tee, while Harrington drove into the left rough. Goosen, who eagled 18 in regulation, knocked his second 35 feet right of the hole. Stenson hit a 6-iron from over 235 yards that landed in the left rough, but bounced 3 feet from the hole. Harrington landed in a greenside bunker.
Harrington blasted out to two feet and Goosen lagged his eagle putt to tap-in range. Stenson calmly stroked home the eagle putt to collect his second win of the season and fourth on the European Tour.
'I thought I better put it away for good,' said Stenson, who won this year's Qatar Masters. 'Sometimes you need the right bounces. It feels great now.'
Stenson posted a 4-under 68 on Sunday to get into the playoff. Goosen fired a 5-under 67, while Harrington, who had a shot to win in regulation but only managed a par on 18, carded a 3-under 69.
David Howell, the overnight leader and 2005 champion, missed a 2-footer for birdie on the 72nd hole to miss the playoff by a stroke. He shot an even-par 72 and tied for fourth place with Martin Erlandsson, who shot a two-under 70 on Sunday. The pair finished at 14-under-par 274.
Stenson began the final round three behind Howell, but made up ground on his front nine. He drained a 12-foot birdie putt at the fifth and made it two in a row with a birdie at six.
Stenson rolled in a 5-footer for birdie at the ninth, a hole he birdied all four rounds, and that tied him for the lead at 14-under par with Erlandsson, Goosen and Harrington.
Several players jockeyed for the lead on the back nine and Stenson held pat thanks to five consecutive pars.
Stenson reached 15-under par with a birdie at the 15th. Howell was already at that number thanks to birdies at six, nine and 11, but Harrington joined the mix thanks to a 25-foot birdie putt at the 15th.
Goosen joined the logjam with an 8-foot eagle putt at 18. Howell fell out of the tie when his 12-foot par putt at the par-4 16th missed left. Stenson missed a short par putt at 17 to fall one behind Goosen and Harrington.
Stenson two-putted for a birdie from 35 feet at the last to join Goosen in the clubhouse at minus-15. It would all come down to the final pairing of Harrington and Howell on the 18th.
Harrington hit his second into a greenside bunker and did well to stop his ball 12 feet past the hole. Howell hit nearly the same spot Stenson did in the playoff, but his ball died in the rough. He chipped to two feet and looked like he would make the playoff.
Harrington's birdie putt for the win stayed above ground, then shockingly, Howell, the Order of Merit leader, badly missed his short birdie putt so it was off to the playoff and Stenson's victory.
This is a good sign for Stenson, who will make his Ryder Cup debut later this month for the European side.
'It was great to be up in contention. It's been a while since I was right up there,' said Stenson. 'It's good practice for what's coming.'
The 10 players who came into the week as the automatic qualifiers for the European side made the team. The European team takes the top five players from the World Points List and the next available five from the European Points List.
Jose Maria Olazabal was fifth on the World Points List, but took the week off to rest. Colin Montgomerie tied for sixth place and moved into fifth on that list.
Luke Donald shared sixth with Montgomerie at 13-under-par 275 and qualified for the team along with Sergio Garcia, Stenson, Montgomerie and Howell. Paul Casey, Robert Karlsson, Harrington, Paul McGinley and Olazabal rounded out the team from the European Points List.
Captain Ian Woosnam will add two players Sunday afternoon.
Markus Brier (67), Robert-Jan Derksen (70), Peter Gustafsson (70), Alexandre Rocha (67) and Simon Wakefield (71) finished knotted in eighth place at minus-11.