At the 1985 World Snooker Championship, Rigitano progressed to the last 48, with wins against Dessie Sheehan (10–9), Bob Harris (10–4), Billy Kelly (10–6), and Mick Fisher (10–2), before losing 8–10 to Neal Foulds. It was the furthest he had progressed in any event in the 1984–85 snooker season, and was his best-ever performance at the World Snooker Championship, and indeed at any major tournament.