Fimiani made his professional debut during the 1992–93 season with A.S. Roma, where he was the team's third-choice goalkeeper, after Giovanni Cervone and Giuseppe Zinetti. After the semi-final game of the Italian Cup against A.C. Milan, Cervone and Zinetti fought in the locker room. Both were disqualified for the finals and Fimiani had to play in both legs of the finals matchup against Torino F.C. Roma lost on away-goals rule (0–3 in Turin and 5–2 in Rome). That was the highlight of his career as he never played on a level higher than third-tier Serie C1 after that season.