The Englishman started the day four shots ahead of Bjerregaard but the Dane carded a brilliant 63 to set the target at 17 under and Fitzpatrick had to birdie the last to take it to extra holes.
The 24 year old then put his approach to 12 feet on the first trip back up the 18th and another birdie saw him become the first player since the late, great Seve Ballesteros to go back-to-back at Crans-sur-Sierre Golf Club.
The final day had developed into an enthralling three-way battle between Fitzpatrick, Bjerregaard and Mike Lorenzo-Vera, with the Frenchman right in it until he bogeyed the last after finding the water.
Lorenzo-Vera finished at 15 under, three shots clear of Spaniard Nacho Elvira and four ahead of England’s Daniel Brooks.
Fitzpatrick needed extra holes to beat Scott Hend in the mountains last season and became just the third player this term to mount a successful defence after Tommy Fleetwood and Brooks Koepka.
At 24 years and eight days old, he also becomes the youngest Englishman to get to five European Tour victories, having won in every season since coming through the Qualifying School in 2014.
For Portugal Masters champion Bjerregaard, the result is a third consecutive top ten, while Lorenzo-Vera has three top tens this season as he looks for a maiden victory.
Japan’s Hideto Tanihara and Chinese Wu Ashun were at ten under, a shot clear of South African pair Darren Fichardt and Charl Schwartzel, American Doug Ghim and Thai Phachara Khongwatmai.
Frenchman Adrien Saddier made the 32nd hole-in-one of the season and second of the week when he holed a seven iron from 192 yards on the 13th.