In the 2013 off-season, Kavaliauskas moved to Spain and signed with Bilbao Basket, team that he played against previous season as a player of VEF Riga. Kavaliauskas spent a part of his 2013–2014 season with the Bilbao Basket before joining Lietuvos rytas Vilnius in 2014. After becoming one of the team's primary players next season, he signed a long-term contract extension with the club in the summer of 2015. During the same summer, he also received identical contract offer from the Rytas biggest rivals in Lithuania, Žalgiris Kaunas, but decided to stay loyal to his hometown club.