Albasini beat Argentine Ariel Maximiliano Richeze and Belgium's Sean de Bie into second and third respectively in a time of 4hrs 35mins 22secs for the 173.4km from Pamplona to Eltziego.
Australian Michael Matthews was fourth and maintains the overall lead after winning Monday's opening stage.
Pre-race favourites Alejandro Valverde and Alberto Contador remain on the same time as Matthews, although Contador had another eventful day as he overcame a puncture after crashing inside the final kilometre on Monday.
Wednesday's third stage gives the climbers a first chance to separate themselves from the pack with six climbs on the 160.5km ride from Vitoria to San Sebastian.
