Rune reached Sunday's decider with a semi-final triumph over top seed Jannik Sinner, who was bidding to win three straight titles in Sofia.
But it was Husler who took the first set, breaking his Danish opponent in the first game of the match before holding in all five of his service games to clinch the opener.
The second set was another tight affair, as both players continued to dominate on their serve. However, the match hit a crucial juncture with Rune leading the second set 6-5, as he spurned two set points to break Husler and level the final up.
Husler survived to take the second set to a tie-break, though Rune again had the opportunity to make it one set apiece as he failed to convert another two set points in the tie-break.
And Husler took advantage with two crucial breaks of Rune's serve to seal the victory and become the first Swiss player to win an ATP Tour title since Roger Federer in 2019.
"I am completely taken aback," Husler said.
"I am lost for words. It was a great match. I played a great, great match for sure. I just tried to stay focused, stayed calm and I am just really happy I was able to make it."