Denmark's Thomas Bjorn holed a 12-foot birdie putt at the first extra play-off hole and emerged from the mist and steady rain with a second victory in the event in three years. It was the third time this season that a Scot had been denied in a play-off
The pair had finished regulation play on 264, 20 under par, with Bjorn carding a 65 to Lee's 67.
The Dane had begun the final day two shots adrift of the man from Bridge of Allan, who had stormed into the lead on Saturday with a course record-equalling 61.
While Bjorn managed to complete his outward half in five under par Lee, after birdieing the first, then had 10 straight pars before finally managing three birdies in four holes from the 11th. In contrast, Bjorn had just one birdie over his closing 10 holes before narrowly missing his birdie putt at the last in regulation.
Lee was on the 17th tee when there was a 30-minute delay because of poor visibility and, when it cleared sufficiently, he parred the hole, then his birdie putt at the 18th from around 25ft hit the side of cup but failed to drop.
In the play-off, Bjorn found the fairway with his tee-shot while Lee was in a fairway bunker, but both players landed on the green some 12 feet from the flag. It was a close call as to whose honour it was before Lee missed his birdie attempt and Bjorn secured a 14th European Tour title.
"I'm pretty proud of my performance. I definitely would have taken second place before the week started, and even after the first round when I was level par," said Lee. "The putter was a bit cold over the first nine today but the good thing was that no-one was running away with it. While Thomas made a charge, he didn't really capitalise on it at the two par-5s, the 14th and 15th, which let me back in it.
"I gave myself a real chance when I birdied those two holes and then, at the last, I still can't believe that birdie putt didn't drop. I could not have hit the putt any better.
"This result lifts a lot of weight off my shoulders: 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. Now I can think about maybe getting ready to go to China for the Final Series instead."
Lee arrived in the Alps struggling with an injury to his left hip and, at 108th on the Race to Dubai, more concerned about holding on to his tour card. His £208,282 cheque is nearly £165,000 more than his previous best and has lifted him to 55th on the Race to Dubai, and a real chance of contesting the lucrative Final Series, starting later next month.
Among the first to congratulate Lee was Ian Stoddart, his Bounce Sports manager, along with another Scotsman, Scott Henry, who stayed on to watch Lee after his own round of 67 left him tied for 34th place on five under par.
Bjorn, who won this event in 2011 and took the Johnnie Walker Championship at Gleneagles a week later, was complimentary about Lee, whom he met for the first time standing on the 18th tee in extra time.
"Craig was unfortunate with his putt on the last hole of regulation and then I did in the play-off what he had been trying to achieve; that's the way golf can be," said Bjorn. "Craig can on be happy with his performance, as he needed to do a lot of things to retain his card and he's done that. That's the first priority for any new guy on the tour. He played tremendous over the weekend and can rightfully be proud."
Stephen Gallacher was the next best of the Scots, signing off with a 68 to share ninth place on 12 under and one shot fewer than Paul Lawrie, who birdied six of his last 10 holes in a 65. Gallacher is 13th on the Race to Dubai with Lawrie 54th, one place ahead of Lee.