Searle had won 14 consecutive sets without reply to reach his first World Championship quarter-final.
The 38-year-old Englishman extended that run to 17 with some clinical finishing in the first three sets against Clayton, who took a scrappy fourth to reduce his deficit.
Searle’s 111 finish in the deciding leg of the fifth, one of his three ton-plus checkouts in the match, restored his three-set advantage and he dominated the seventh set to secure a spot in the last four.
Clayton scored better for long spells of the quarter-final but too many missed attempts on the outer ring proved costly for the Welsh fifth seed, who landed just 10 of his 40 attempts at doubles (25%).
Searle, in contrast, hit 17 of his 30 attempts (56.7%).
Searle lives with dominant optic atrophy, a genetic eye condition which affects his vision and for which he wears contact lenses.
Speaking to Sky Sports on stage after his win, he said: “I can’t see particularly well.
“Other people who try to play darts, if they can’t see particularly well, try not to let that hold you back.
“I try to be an inspiration to them.”