Cross-sectional studies have shown the connections between oral language, reading, and writing skills, but there has been limited longitudinal research, especially in primary school. This study examined the relationships between oral narrative, reading, and writing skills in a longitudinal sample of 80 Italian-speaking primary school children (M-age at Time 1 = 8.57 years, SD = 0.53; 52 boys, 28 girls). The time frame of the study was one and a half years (two school years). Data collection was divided into three time points, T1 at the beginning of the school year, T1bis at the middle of the same school year, and T2 at the beginning of the subsequent school year. Measures collected were: oral narrative competence at T1, cognitive-lexical skills at T1bis, and reading and writing skills at T2. Reading and writing skills were also acquired at T1 as control variables. Moderate mediation models showed oral narrative competence directly predicted reading and spelling accuracy, while the interaction between oral narrative and cognitive-lexical skills significantly influenced outcomes (reading and spelling accuracy). Our findings extend knowledge about oral, reading, and writing domains' longitudinal connections in primary school and specify the important moderating role of cognitive-lexical skills in the relationship between oral language and literacy skills.