Óscar Tabárez, then-coach of Italian side Cagliari, was impressed by Suazo's performance and did not hesitate in bringing him to Europe, for US$2 million transfer fee and US$200,000 tax to National Autonomous Federation of Football of Honduras, as well as 15–20% of the future capital gain if Cagliari sold the player above the US$2.2M price tag. Suazo officially joined the club ahead of the 1999–2000 Serie A season. In his first year with the team, he scored one goal in 13 league appearances, and at the end of the 1999–2000 season, Cagliari were relegated to Serie B, where they would remain until the 2003–04 season. In four years in Serie B, Suazo played 113 matches and scored 40 goals for the club. His scoring efficiency was impressive enough for him to earn the nickname "La Pantera" (the Panther). Suazo's time in Serie B provided him with great experience which would help ease his transition into more difficult competition at the top of the Italian Lega Calcio.