Fitzpatrick, 24, who was overlooked as a European Ryder Cup wildcard earlier this week, confidently rolled in a 10-foot birdie putt on the 18th to secure victory, becoming the first player since Seve Ballesteros in 1978 to win back-to-back European Masters titles.
The Englishman started the day four shots clear of Bjerregaard, but had to birdie the final hole of his round at Crans-sur-Sierre to force the playoff with the Danish player, who shot a brilliant 7-under-par 63 to briefly hold the outright lead.
Although Fitzpatrick started the day in front, the landscape quickly changed after the first few holes in the Swiss Alps. Frenchman Mike Lorenzo-Vera, who was Fitzpatrick's closest competitor at two behind, made the perfect start with a birdie at the 1st while Fitzpatrick dropped a shot for the first time in 34 holes with a bogey at the par-3 3rd.
This, added to the fast start of Bjerregaard, meant it was a three-way battle from the start. Bjerregaard also birdied the 1st, before adding four more birdies on the front nine to move to 15 under at the turn.
After dropping a further stroke at the 6th, Fitzpatrick recovered with birdies at 7 and 9 to move back to even par for his round. Lorenzo-Vera also birdied the 9th, but then gained a further shot at the 10th to take the outright lead at 16 under.
An excellent approach from Fitzpatrick at the 12th allowed the Englishman to move to within one shot of Lorenzo-Vera as the group headed to the par-3 12th. Fitzpatrick's tee shot was closest to the flag but it was Lorenzo-Vera who came away with the birdie after an excellent downhill putt moved him two strokes clear.
Everything changed again as the leaders advanced to the back-to-back par 5s at 14 and 15. Bjerregaard was already clear, making birdies on both holes to move to 17 under overall. The Dane then finished with two closing pars to take the clubhouse lead.
Poor shot selection from Lorenzo-Vera led to a double-bogey 7 at the 14th, although the Frenchman immediately bounced back with a birdie at the next hole. Fitzpatrick also gained a shot at the 15th and suddenly the pair were tied, both on 16 under but both a shot behind Bjerregaard with only two holes remaining.
After pars at 17, both players had to go for broke with their approaches on the last. Fitzpatrick pitched to within seven feet while Lorenzo-Vera could only find the water from the fairway bunker, his tournament hopes disappearing in the process.
Fitzpatrick held his nerve to sink the vital birdie putt, before he repeated the act in the playoff to win his first European Tour title of this season and the fifth of his career.