Perasović was born in Stobreč, in the former Yugoslavia. He started playing basketball at the age of 14, and was soon recruited by KK Split, then named Jugoplastika, in 1981.
Perasović was member of the Yugoslav junior national basketball team which won the silver medal in the junior European championship in Bulgaria in 1982, and the bronze medal in Sweden in 1984.
His club went on to win three Euroleague Championships, in 1989 and 1990 as "Jugoplastika" and in 1991 as "Pop 84". In 1988, 1989, 1990 and 1991 they also won the Yugoslav basketball championship. In 1990 and 1991 they won the Yugoslav basketball cup, and in 1992 the Croatian basketball cup (that time as "Slobodna Dalmacija").
Perasović was part of the famous national team of Yugoslavia that won the World Championship in Argentina in 1990, and the European championship in Italy in 1991. He played for the Croatian national basketball team when they won the silver in the Barcelona Olympics in 1992, the bronze medal in 1994 World Championship in Canada and the European bronze medal in Germany in 1993 and Greece in 1995.
In 1997 he moved to Fuenlabrada where he played until 2002, then moved to Alicante, and finally retired from his playing career in 2003. In his career in Spain, he won the award for the best scorer of the Spanish league several times, was once the best scorer of the Radivoj Korać Cup, and participated in several ACB All Star games.
He became the manager of KK Split for a while, before moving back to Spain to become the manager of TAU Cerámica. He led the team to the Euroleague Final Four.
In the 2007-08 season he became the coach for CB Estudiantes, filling in for Mariano de Pablos, who had been fired due to negative results, and succeeded in keeping the team in the Spanish league.
He then moved to Zagreb, Croatia, to become the KK Cibona coach in the seasons 2008-09 and 2009-10. In 2009 he led the team to the Adriatic League final, winning the award for the best coach in the Adriatic League in 2008-09 season, and won the Croatian cup and championship, respectively. He again took Cibona to the Adriatic League and Croatian cup finals in 2010, and won the Croatian championship, making Cibona the first team in the Croatian championship history to overcome a 0-2 deficit in a best-of-five playoff series. He reached Euroleague Top 16 phase in both seasons with Cibona.
In January 2012, he comes back to Spain to coach Valencia BC.