In the 2004–05 Serie A season, Suazo scored seven goals in 22 matches in a 4–3–3 scheme in which he performed as a reserve behind Gianfranco Zola, Mauro Esposito and Antonio Langella. Suazo's scoring proved vital in helping Cagliari avoid relegation and impressed top clubs across Europe, despite only scoring six goals. In 2006, he became a starter for Cagliari and scored 22 goals in Serie A. For his play that season, Suazo was honoured with the Serie A Foreign Footballer of the Year, which he shared with Milan's Kaká. In 2007, Suazo continued his great play for Cagliari, where he scored 18 more goals in the Serie A and helped save Cagliari from another relegation to Serie B. During his spell with Cagliari, Suazo was known for his attacking partnership with both Langella and Esposito.