Perasović's club, KK Split, 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 League championship. In 1990 and 1991, they also won the Yugoslav Basketball Cup, and in 1992, they won the Croatian Basketball Cup. In 1992, Perasović moved to the Spanish club Breogán, and he spent one season there, before moving to the Spanish club Taugrés, in 1993. He won the 1995 Spanish King's Cup and in 1996, he won the Saporta Cup against PAOK. In 1997, he moved to the Spanish club Fuenlabrada, where he played until 2002. He then moved to the Spanish club Alicante, and he finally retired from his basketball playing career in 2003. During his playing career in Spain, he won the Spanish ACB League Top Scorer award five times. He was also once the best scorer of the Radivoj Korać Cup, and he participated in several Liga ACB All Star games.
Perasović became the manager of Split CO for awhile, 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 head coach of Estudiantes, filling in for Mariano de Pablos, who had been fired due to negative results. He succeeded in keeping the team in the Spanish league. He then moved to Zagreb, Croatia, to become the head coach of Cibona, 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 the 2008–09 season, and he won the Croatian Cup and Croatian League championship, respectively. He again took Cibona to the Adriatic League and Croatian Cup finals in 2010. He also won the Croatian League championship, making Cibona the first team in the Croatian League's history to overcome an 0-2 series deficit in a best-of-five playoff series. He also reached the EuroLeague Top 16 phase in both seasons with Cibona. In January 2012, he came back to Spain to coach Valencia. Perasović won the 2013–14 EuroCup, and left the club in January 2015. In March 2015, Perasović took over the senior Croatiamen's national basketball team. After a disappointing EuroBasket 2015 tournament, in which Croatia was defeated in the Round of 16, Perasović and Croatia parted ways. In June 2015, he came back to Spain to coach Laboral Kutxa, and in February 2016, he extended his contract with Baskonia through the 2016–17 season. After being a semifinalist of the three competitions, Baskonia played (EuroLeague, Copa del Rey, and Liga ACB, Perasović left the club and went back to Anadolu Efes. On December 16, 2017, Anadolu Efes parted ways with him. On November 16, 2018, he came back to Spain to third time to coach Kirolbet Baskonia until the end of 2019-20 season to replace Pedro Martínez.