For Allen it was a second straight first-round defeat at the World Championship, while for Clarke it was comfortably the Welshman’s biggest win of his career.
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Clarke - who even tweeted Jimmy White during the interval on Tuesday evening - was the lowest ranked player heading into the main draw at 89, having overcome Joe Perry among others in qualifying.
But the size of the first-round task did not daunt Clarke, who hit a 136 and crucially won four straight frames on Tuesday night en route to victory - with a second-round match against Anthony McGill up next.
Jamie Clarke stunned by 'absolutely crazy' World Championship win over Mark Allen
Five centuries not enough for Allen
Allen narrowly led 5-4 after the first session, with breaks of 136, 105, 122 and 104 helping him take that slender lead with him into the evening’s action.
A fifth century of the match, a 105, saw Allen extend his advantage to 6-4 before Clarke produced an unlikely comeback.
Four frames on the spin, including a 53 and 80, helped Clarke move 8-6 in front, and though he spurned a chance to make it 9-6 he held his nerve to take the next frame.
At 9-7 Allen knew he had to win three frames without reply, he managed the first with a 76, but Clarke got over the line after a tense 18th frame.
Watch Jamie Clarke close out shock World Snooker Championship win over Mark Allen