In 1984 he was a member of the Yugoslav handball team which won the gold medal. He played all six matches as goalkeeper. Four years later he was part of the Yugoslav team which won the bronze medal, playing five matches.
In 1985 and 1986 he was a member of European Champions Cup winning team of RK Metaloplastika. With Metaloplastika he also won 7 Yugoslav national titles. He also played an additional ECC final with the club and reached three more semi-finals and a Cup Winners' Cup semi-final. Throughout the 1980s Bašić was considered one of the best goalkeepers in the game.[3] In 1989 he left Šabac to go play for Medveščak Zagreb for one season. With club he won the Yugoslav Cup that season.
In 1996 he returned to the scene with Badel 1862 Zagreb where he played for five years winning five league and four cup titles also reaching the EHF Champions League final three times.[6] After a season and half in RK Medveščak he ended his career in 2003 at Fotex Veszprém.[7]
Personal life
He is the father of professional handball player Sonja Bašić.