At the weather-hit mountain course at Crans-Montana, Bjorn holed a 12-foot putt to defeat Scotland's Craig Lee in mist and steady rain after both players ended regulation play tied at 20-under par.
It is the two-time Ryder Cup winner's 14th career victory but first in two years while Lee was looking to capture a maiden Tour title.
Frenchman Victor Dubuisson shot a final round 66 to finish alone in third on 19 under while Spaniard Alejandro Canizares was a further shot back in fourth.
"It was nice," said the relieved Dane after closing out victory on the first play-off after Lee found the bunker with his tee shot on the 18th which gave him a tough approach to the par four green.
"When I get into situations like today (Sunday) I really know to grind it out and I have to say I've been pretty good at closing out tournaments in my career," he said.
"I give everything in those situations and I just grind, and grind and grind even knowing that I don't need to play great.
"That's what it's about late on Sunday afternoons and I've just got that in me."
Victory earned Bjørrn a first prize cheque of 366,660 euros and will lift him from 66th to 45th in the world rankings.
"This year I have come up short a few times including the hurt in Munich but I came here really desperate to win this golf tournament so this one is very sweet for me given I am 42 years of age," he said.
"I had two bogeys in 72 holes, which is good going around here," Bjørrn said.
"I felt good and I got over the line," he said.
"It was nice to do that in a playoff.
"I've had a hard time dealing with pressure situations and there is no more pressure than that."
It was had on Lee who equalled the course record on Saturday with a sensational ten under par 61 that sent him into the final day with a two-shot lead.
Bjørrn needed just nine putts over the front nine to take the clubhouse lead but Lee hit back with three birdies down the stretch and agonisingly saw his birdie stroke for victory lip out at the final hole which sent the pair to a play-off.
"You keep thinking when is going to be the next win but then you play alongside someone like Miguel (Angel Jimenez) and he seems like he's 60-odd and away you go and that gives you more confidence," continued Bjørrn.
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Jimenez finished tied for fifth with Englishman Ross Fisher five shots back.
The victory puts Bjørrn top of the Ryder Cup qualifying points table after two weeks of qualifying.
Despite Lee's disappointment the Scot jumped from 108th to 55th on the Race to Dubai and the assurance of retaining his Tour card for next year.
"This result lifts a lot of weight off my shoulders as my card is now secure for next year and it means I don't have to go chasing tournaments like heading to Perth in Australia later this year," said Lee.
"Now I can think about maybe getting ready to go to China for the 'Final Series' instead."