The 32-year-old Swede held his nerve to beat South African Retief Goosen on the first hole of a sudden-death play-off and claim the pounds 120,000 first prize after the pair had finished tied, 14-under, on 274 following matching 68s.
It looked as though the Spanish Open champion had thrown it all away after fluffing a chip on the 17th to lose the lead for the first time since Friday.
But he holed a brave putt to drop only one shot and then repeated the trick on the last before Goosen missed from only three feet on the 18th to take it into sudden death.
Another superb pressure putt from 10 feet at the extra hole then completed a remarkable victory as Goosen bogeyed the 18th for the second time in 20 minutes.
"It's hard to put into words what qualifying for the Ryder Cup means," said Sandelin who climbed to third in the points table and will follow in the footsteps of compatriots Joakim Haeggman, Per-Ulrik Johansson and Jesper Parnevik against the Americans at Boston in September.
"It's a great feeling to qualify for the Ryder Cup especially after I got an invitation to play in the USPGA earlier this week, so now I'm set for the rest of the year.
"It's the big team event you want to play in because you play for the team and not yourself. It's always good to play together and you get closer to the other guys.
"I know it's going to be tough but hopefully I can handle it, for sure I'm a lot better prepared than a couple of years ago. Everything is well organised now and I don't have to waste too much energy on things outside golf."
Goosen's missed putt cost him the chance to overtake Colin Montgomerie in the standings.
Sweden's Pierre Fulke finished third on 12 under with Germany's Thomas Gogele and South African Roger Wessels a shot further back.
England's Gary Evans and Scotland's Raymond Russell, who started the day joint second, could only manage level par 72s to finish in a tie for ninth alongside David Carter, who closed with a 69.
Evans was bitterly disappointed not to get closer to claiming a maiden win after eight years on tour but at least had the consolation of winning a Rolex watch worth around pounds 3,000 for his course record 62 in the first round.
"I'm very disappointed," said the 30-year-old from Worthing. "I played really nicely and did everything right but didn't hole anything. I felt I deserved more than I got out of the week - apart from the Rolex."
After 20 missed cuts on the European PGA Tour, Justin Rose finally made it into the third round of a competition this weekend, firing a closing five-under-par 65 to finish fourth on his Challenge Tour debut, in Austria, collecting in the process his first pay cheque - for pounds 2,681.
Rose's 13-under-par 267 was four strokes away from a play-off between Juan Ciola of Switzerland and New Zealand's Elliot Boult. That particular contest went to two extra holes before Ciola holed from five feet for a birdie three to take the top prize of just under pounds 9,000.
"It's been a good week," Rose said. "That's my lowest 72 hole total and I've never finished 13 under before. I knew I had to shoot low today to stand any chance, something like a 63. But even that wouldn't have been good enough.
David Frost, who equalled the PGA's record low score for 36 holes with consecutive 63s in the first two rounds of the St Jude's Classic in Memphis, lost his magic touch in the third round on Saturday night.
Frost failed to post a birdie during a three-over-par 74 which allowed Hal Sutton, Tom Lehman, Tim Herron and Ted Tryba to surge past him. Masters champion Jose Maria Olazabal was six shots off the pace.
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