Born in Zagreb, Šarić competed for Yugoslavia at the start of his career and played his first Grand Prix tournament at the Stuttgart Open in 1986.

Ranked 800 in the world, he was given a wild-card into the tournament because he played for a local club and caused an upset by beating American Brian Teacher to make the second round.

In 1993 he featured in the main draw of the Romanian Open, the only other time he played singles in what had by then become the ATP Tour.

In 1994 he was a member of the Croatia Davis Cup team that defeated Portugal in a qualifier which secured them a spot in the World Group.

Teammates Goran Ivanišević and Saša Hiršzon were favoured in the other fixtures and the Croatian side finished the tournament as runners-up to Sweden.