He landed checkouts of 164 and 161 on his way to coming through a stern test against Chisnall.
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Chisnall held the advantage at 6-4 but, two legs later, the scores were level as Price punished Chisnall’s unsuccessful 76 attempt with a 124 checkout on the bullseye.
That passage of play proved pivotal as the following leg saw Price go in front; a lead which the Welshman never relinquished despite checkouts of 142 and 111 from Chisnall who kept the pressure on to the end.
Price will now take on Jose De Sousa, who broke down in tears after defeating Rob Cross 11-8 to reach the last eight for the first time.