Žilić started out at OFK Kikinda, joining his hometown club as a trainee in 1985. He made his senior debut in the 1992–93 season, as they suffered relegation from the top flight. After four seasons in the senior squad, Žilić was transferred to Vojvodina. He was a member of the team that reached the final of the 1998 UEFA Intertoto Cup, losing 1–2 on aggregate to Werder Bremen. In June 2000, Žilić moved abroad to Bulgaria and signed a three-year contract with CSKA Sofia. He left the club by mutual agreement in February 2001, recording only one league appearance for the side. In July 2001, Žilić returned to his homeland and joined ambitious Sartid Smederevo. He spent the following four seasons at the club, winning the Serbia and Montenegro Cup in 2003. In July 2005, Žilić completed a controversial move to Croatian side Rijeka. The transfer caused a minor sensation in the region as it marked the first occasion that a player of Serb ethnicity joined a Croatian club after the Yugoslav Wars. Despite being exposed to severe verbal abuse by the nationalist supporters of Rijeka, Žilić immediately established himself as the first-choice goalkeeper and gradually earned the support of fans with his consistent performances. He eventually helped them win the 2005–06 Croatian Cup. On 29 November 2006, Žilić scored a 92nd-minute header against Konavljanin that got Rijeka into the 2006–07 Croatian Cup semi-finals. By fall 2008, Žilić lost his place in the first team and got demoted to as low as training with the youth team. He finally left them in the 2009 winter transfer window and moved to Slovenian club Gorica.
International career
Žilić made his international debut for FR Yugoslavia on 23 September 1998, coming on as a second-half substitute for Ivica Kralj in a 1–1 away friendly draw at Brazil, while keeping a clean sheet in the process. He collected a total of eight caps for his country between 1998 and 2003.
Post-playing career
In December 2012, Žilić became the president of OFK Kikinda. He resigned from the position a little bit less than a year later.
