Perry's breakthrough came when he reached the final of the European Open in 2001. He first reached the quarter-finals of the World Championship in 2004, beating then defending champion Mark Williams 13–11 along the way, also making the tournament's highest break of 145 (which remains Perry's best in competition), before losing to Matthew Stevens. He repeated this run in 2008 when he defeated Graeme Dott and Stuart Bingham, and bettered it by going on to beat Stephen Maguire 13–12 and earn his place in the semi-finals, which he narrowly lost to Ali Carter. Previously, he had also reached the last 16 on his Crucible debut in 1999, beating Steve Davis on the final black in the last 32.