As the world number 72 for the 2001/2002 season, Dunn enjoyed his best form yet at the 2002 World Championship, defeating Stephen Croft 10–2, David McDonnell 10–8, Lee Walker 10–2, David Finbow 10–5 and Billy Snaddon 10–9 - having trailed 1–5 - to qualify for the main stages at the Crucible Theatre for the first time. Drawn against Stevens, he came to trail 1–7 and, although he recovered well to 6–9, could not prevent a 6–10 loss. Nevertheless, the performance earned Dunn £14,500, and he broke into the top 64 as a result.