Anderson is aiming to win a maiden World Matchplay title and was installed as the tournament favourite after Michael van Gerwen suffered a shock defeat in the first round.
The 47-year-old saw off Stephen Bunting and Raymond van Barneveld in the previous rounds to set up a tie with Cullen.
And the tie got off to a thrilling start when Cullen threw a 10-dart leg.
But Anderson went one better straight after with the perfect leg, using only nine darts to check out from 501.
He hit seven consecutive T20s before going down to T19 and throwing D12 to achieve the rare feat.
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Not only did the nine-darter get the crowd on their feet, but Anderson also pocketed a healthy £45,000.
Anderson’s nine-darter in a competitive tournament came back in the 2016 World Championships.
Jeffrey De Zwaan beat Dave Chisnall earlier today to book his place in the semi-finals.
Tomorrow evening sees Simon Whitlock take on Peter Wright before Mensur Suljovic faces Darren Webster.