The OricaGreenedge prevailed in a bunch sprint after a hilly 172.5km ride from Moutier to Porrentruy, including the category two Col de la Croix.
He finished ahead of in-form Frenchman Julian Alaphilippe and Italy's Damiano Caruso.
Albasini took the yellow jersey from Welsh rider Geraint Thomas on Wednesday and now holds a 20-second lead on his teammate Ivan Santaromita of Italy and Sky's Chris Froome, who has won the last two editions of the Tour de
The Brit remains one of the favourites to win the Tour, which ends on Sunday.
Friday's fourth stage will take the peloton on a 169.8km ride from Neuveville to Fribourg, ahead of Saturday's difficult mountain stage.