He finished ahead of Diego Ulissi (UAE Team Emirates) was second with Jesus Herrada (Movistar) in third.
“It is a great victory today,” 36-year-old Albasini said. “It was not easy to win today coming straight from the classics as that was a big goal and it takes a lot of mental energy.”
“I really needed to focus coming to this race to suffer and to fight. It is Romandie so it is important I can come here and race well, so I am very happy that I could take the win today.
“I wasn’t so confident for today’s stage but I told myself if I can be there at the end in Liege-Bastogne-Liege after 4,000metres of climbing then why can’t I be able to be here over the climbs today.
“I tried to fight and stay in the bunch and it worked out to be even better than I thought so I am really happy with that.”
Fabio Felline (Trek-Segafredo) , who won the 4.8km prologue, finished safely in the bunch to retain the overall lead. Maximilian Schachmann )Quick-Step Floors) jumped two places to second overall at 8sec with Herrada now third on the same time.
Climbing towards the finish in Champery in poor visibility the attacks started inside the final kilometre of the 173.3km stage from Aigle with several big names including Tour de France champion Chris Froome in the mix.
It was the Swiss rider Albasini who proved the strongest though as he powered through the wet to cross the line clear in first place and for his seventh career stage victory in the race.
Matvey Mamykin (Katusha-Alpecin), Sander Armee (Lotto-Soudal), Mekseb Debesay (Dimension-Data) and Marco Minnaard (Wanty Gobert) were the four riders who made a break stick, with the foursome managing an advantage of eight and a half minutes at one stage before finally giving up the fight with six kilometres to go.
Stage 2 takes the peloton 160.7km from Champery to Bulle.