Fagan failed to make an impact at the 1978 Masters, losing 2–4 to John Pulman in the first round. At the 1978 World Snooker Championship he beat John Dunning 9–5 and then Alex Higgins 13–12. In the match against Higgins, Fagan was 10–12 behind but won two frames on the black and the last on the pink. He lost 10–13 to Fred Davis in the quarter-finals.