The scheduled 203-kilometre ride between Ascona and Sion was reduced to just 88 kilometres from Bigerbrad because of snow on the Simplon Pass, and Orica-Greenedge rider Albasini triumphed in a sprint after two hours, 11minutes and 11 seconds ahead of Spain's Jesus Herrada and Lithuania's Ramunas Navardauskas.
"The objective was to win a stage, and I have already done it.," Albasini told Swiss television after what was the first Swiss win in the race for ten years.
"But you can't ever settle for what you've got, you must always want to win.
Michal Kwiatkowski of Poland, who won the prologue in Ascona on Tuesday, retained the overall race lead but he is only five seconds ahead of Albasini.
Britain's Chris Froome, who won the Tour of Romandie last year before going on to win the Tour de France, is 10th overall, 14 seconds off the pace.
Thursday's second stage will be 166.5km from Sion to Montreux, which is likely to finish in a sprint and so could favour Albasini once again.
The six-day event concludes on Sunday.