Mornar was born in Split. In Mornar's final season at Anderlecht, he scored their goal in a 1–1 home draw against Bayern Munich on 30 September 2003. The player was offered a new two-year contract by Anderlecht, but opted to move across the English channel to Portsmouth. He moved to the Premier League at the end of January 2004 for £500,000, signing a two-and-half-year deal. Mornar made his Pompey debut in a goalless draw at home to Wolverhampton, and looked lively. He then scored his first and only goal in the next game against Tottenham. A performance that earned Mornar the 'Swan d'Or', a celebrated Croatian sporting award. He played as a winger in most of his Portsmouth appearances. However, Mornar failed to recreate his previous form at Portsmouth. Seemingly out of the pictureat the club, he was loaned to Rennes of the French Ligue 1 for the 2004–05 season, with then Pompey manager Harry Redknapp saying that. he would allow Mornar to be sold upon his return, although this was not well received by the fans who admired his tireless running on the wings. Although it appeared that Mornar was in new boss Alain Perrin's plans for the 2005–06 campaign, he was thwarted by hamstring injuries throughout the season. Upon the return of Harry Redknapp as manager in December 2005 it looked as though Mornar's contract would be allowed to expire the next Summer. However, it transpired that there was a clause in his contract guaranteeing him a further year at the club should relegation be avoided and he remained a Portsmouth player, until September 2006 when his contract with the club was cancelled by mutual consent. This brought further complications due to the fact that Mornar could not find a club willing to sign him. Despite his unceremonious exit from Portsmouth he enjoyed his time playing there and persuaded fellow Split native Niko Kranjčar to join the club. Reportedly he offered his services to first league teams from Belgium, Scotland, Portugal and Japan but no team was interested, thereby forcing his retirement.
International career
Mornar was capped 22 times for Croatia and scored one goal for his country.