Williams, making his fifth successive appearance in the championship, although he had to qualify this year, said: "I started like a house on fire and I'm normally a slow starter.
"I won six of the first seven legs but then I probably went to sleep. In the final set I knew it was essential to break Matt. I didn't want to get into a tie-break situation."
Clark won the first leg of the fifth set, but Williams held his darts to make it 1-1 and then, helped by a maximum 180, broke his rival to lead 2-1.
Then, needing to hold his darts again for victory, he gave Clark no chance to shoot for a double, checking out with a 64 after another maximum had helped him on the way.
Andy Fordham provided a mild shock when he beat sixth-seeded Mervyn King 3-2 - despite his rival having six 180s during the match.
King, from Ipswich, invariably scores high but Fordham, landlord of the Queen's Arms in Woolwich, clinched a keenly contested match because of his deadlier finishing, landing 12 doubles in only 22 attempts.
"I was worried about not finishing well because I know how well Mervyn can score," Fordham said.
"But I think that was the best I have played in the Embassy, even though I've been a semi-finalist twice."
Results, Digest, page 23Reuse content