Kurz ended up winning 3-1 to continue Cullen's dismal run on the Alexandra Palace stage as he hit a 93 average and 42 percent on doubles on his way to victory.
To begin, Kurz missed two darts for the set and Cullen completed it coming from 2-0 down to snatch it in a decider and take the lead as the German equipped himself well in the early going.
A second 116 checkout from Cullen saw him hit the front in the second set and he broke throw from there to go 2-0 up but Kurz came back brilliantly to claim the set taking it in the decider to go 1-1.
Cullen broke again in the next set but Kurz was up to the task going 2-1 up and he clinched the set from there 3-1 to go one set away from victory.
The Bradford ace went 2-0 up again but the doubts would have crept in and this was right as Kurz made it 2-2 to go one away and he showed great temperament to tame the wall of boos to win the tie.
Click here for more information on the PDC World Darts Championship, which takes place at the Alexandra Palace between December 13 and January 1.
Nathan Aspinall (95.38) 3-1 (90.92) Danny Baggish
Joe Cullen (92.47) 1-3 (93.05) Nico Kurz
Max Hopp v Benito van de Pas
Peter Wright v Noel Malicdem
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