At the 1980 World Snooker Championship he reached the quarter-finals, defeating Patsy Fagan and defending champion Terry Griffiths before losing to Alex Higgins 9–13. He won his first major title that year, the 1980 UK Championship, beating Griffiths 9–0 in the semi-finals and Higgins 16–6 in the final. After winning his first title, he won the Wilson's Classic in 1980, the Yamaha Organs and English Professional in 1981, and was the bookmakers' favourite to win the 1981 World Snooker Championship despite being seeded 13th. Davis reached the final by defeating White in the first round, Higgins in the second round, Griffiths in the quarter-finals and defending champion Cliff Thorburn in the semi-final. In the final, he won 18–12 against Doug Mountjoy to take his first world championship. Davis completed a 9–0 whitewash victory over Dennis Taylor in the International Open final and retained the UK Championship with a 16–3 win over Griffiths in the final, winning five events in 1981. In January 1982, Davis compiled the first televised maximum break at the Classic at Queen Elizabeth Hall in Oldham against John Spencer. As Lada were sponsoring the event, they offered Davis a car for completing the break. He reached the final, but lost 8–9 to Griffiths in the final. However, later that month Davis defeated Griffiths 9–5 in the Masters final, to win his first title.