Cullen had a very flashy start in his quarter-final, taking a 5-0 lead before Gurney came back to 6-3.
After that, both players held their own leg a total of eight times before another two breaks could be recorded.
At 10-8, Gurney missed the chance to come all the way back into the match and at 12-10 he failed to cash in another break. Leading 15-11, Cullen (91.11 average and eight 180s in 27 legs) managed to break his opponent for the seventh time and make it 16-11 to win the match.
The match sequence at the second quarter-final was similar, although Dobey initially took another 4-2 and 6-3 lead. With the score eventually balanced a 7-7, Aspinall - world number nine - struck again.
From 8-8, he ran out to 14-8 before Dobey was able to do answer back and cut the deficit to 14-10 and then 15-12.
In the final set, it was a break from Aspinall that won the game. The winner had an average of 99.33 and threw 180 10 times in 28 legs.
The other two quarter-finals are scheduled for Friday night. At 20:10 EST, Englishman Ryan Searle (world number 15) faces Welshman Jonny Clayton (number seven). Following that, Luke Humphries (number six) plays Damon Heta (number 13).
