The Englishman had entered the final round with a two-shot advantage but Dane Bjerregaard carded a stunning seven-under-par 63 to set a target at 17-under overall.
Courtesy of a perfect approach to 12 feet, Fitzpatrick holed a birdie at the 18th to finish the final round on three under and take it to extra holes.
Another birdie at the same hole ensured he became the first player since Spanish great Seve Ballesteros in 1978 to win back-to-back titles at Crans-sur-Sierre Golf Club in Switzerland.
“This is what I wanted to achieve this season – another win,” said Fitzpatrick.
“To get it here again is so special and to get my fifth is amazing. I love this place.
“Of all my wins I’d say that was definitely the most difficult. I didn’t have my A game today; despite loving this place I just didn’t play my best today.
“I managed to grind it out, made some crucial birdies coming in and I’m delighted.”
At 24 years and eight days old, Fitzpatrick becomes the youngest Englishman to achieve five European Tour victories, having lifted a title in every season since coming through qualifying school in 2014.
Frenchman Mike Lorenzo-Vera finished third with 15 under for the tournament, three shots clear of Spaniard Nacho Elvira and four ahead of England’s Daniel Brooks.
And Fitzpatrick has no issues with being left out of the Ryder Cup.
European skipper Thomas Bjorn chose to go with experience for his four wild cards, picking Ian Poulter, Paul Casey, Henrik Stenson and Sergio Garcia, meaning Fitzpatrick will have to wait to add to his 2016 appearance.
Asked if he had any regrets at missing out, he said: “Not at all, genuinely I don’t.
“I didn’t play well enough this summer, it’s as simple as that.”