Born in Zagreb, Marić began his professional career at Dinamo Zagreb in 1992. In the autumn of 1998, he appeared for Dinamo Zagreb in all of their six group matches in the UEFA Champions League and secured himself a move to English club Newcastle United on 4 February 1999 for a transfer fee of $5.8 million. He made his Premier League debut for Newcastle United on 10 March 1999 against Nottingham Forest, but never established himself as a regular in the side and, after making 23 Premier League appearances without scoring, moved to Portuguese club Porto in 2000. At Newcastle United, he was the first Croatian player to appear in an FA Cup Final, when he came on as a substitute in the Magpies' 2–0 defeat to Manchester United in the 1999 Final. During the final, with Newcastle trailing 2–0, Marić weakly shot past the post when exceptionally well placed to score. This summed up his Newcastle career in general. He did, however, score twice for Newcastle in their 1999-2000 UEFA Cup campaign, when he netted both home and away against Zürich.