In his first professional match, in the qualifying competition for the 1978 UK Championship, Griffiths lost 8–9 to Rex Williams after leading 8–2. Williams took a 2–1 lead, before Griffiths won the next seven frames, and Williams took the following seven. In the , Griffiths rushed when potting the and went , a shot. Williams later potted the pink to secure victory. After qualifying for the 1979 World Championship, by eliminating Bernard Bennett 9–2 (from 0–2 behind) and Jim Meadowcroft 9–6 (from 6–6), Griffiths defeated the previous year's runner-up Perrie Mans 13–8 in the first round and Alex Higgins 13–12 in the quarter-finals. After beating Eddie Charlton 19–17 in a long semi-final that finished at 1:40 am, Griffiths told interviewer David Vine "I'm in the final now, you know." In the final, he faced Dennis Taylor, who, having been a professional since 1973, was also playing in his first world championship final. The match was close for the first four of the six , and the match was level at 15–15 before Griffiths took a 17–16 lead and went on to win 24–16, becoming world champion at the first attempt, in only his second tournament as a professional. He was only the second player to win the championship after playing in qualifying, after Higgins in 1972, and the first to win it at the Crucuble as a qualifier. The only other player to achieve this, as at 2021, was Shaun Murphy in 2005.