Cullen kicked off with a 5-2 defeat of Keegan Brown, whose threw a 170 checkout despite a lack of sleep as he continues in his role as an NHS worker.
Welshman Cullen averaged 106.2 in an impressive defeat and that would prove a benchmark he was able to reach all night, while others were not.
Brown, who lost connection in his first attempt in the competition before failing to qualify second time around, said: "Everyone is playing as good as they can, but it is good to play darts as a group again. Win or lose, we are happy playing."
Cullen reacted by saying "I told you I was up for it!" and went on to underline that point with a 5-3 defeat of compatriot Price, this time registering an average of 107.6, in a match that featured seven maximums.
Price said: "Joe has played brilliant there. I played alright in patches. Joe was more consistent than me. He probably deserves to win this group."
And so he did, Cullen going on to whitewash Bradley Brooks, adding a further five maximums in the process for a 106.65 average on the night.
All four players were having their second bites of the cherry having failed to win previous groups, and Price was favourite to become the 31st player through to the last 32.
However, despite rallying to beat Brooks 5-3, defeat to Cullen effectively ended his bid and the world number three - who admitted to being short of practice as he focuses on DIY and gardening - went on to lose 5-4 to Brown in the final match of the night.
Price said: "I played alright in a couple of my games, but it wasn't enough in the end. It is not a PDC Tour I like to play in. It is a bit of fun, but I am giving my best, my all."
Brown added: "It is hard to get motivated for the last game with nothing on it, but it was nice to get a win. Darts is not my number-one priority at the moment, the hospital is."
The final qualifier will be determined on Monday, when Peter Wright stars in Group 32.
PDC Home Tour Darts: Sunday results and Monday fixtures
Group 31 - Sunday May 17
- Gerwyn Price 5-3 Bradley Brooks
- Joe Cullen 5-2 Keegan Brown
- Bradley Brooks 1-5 Keegan Brown
- Gerwyn Price 3-5 Joe Cullen
- Joe Cullen 5-0 Bradley Brooks
- Keegan Brown 5-4 Gerwyn Price
GROUP STANDINGS
- Joe Cullen P 3 W 3 L 0 Leg Diff +10
- Keegan Brown P 3 W 2 L 1 Leg Diff +2
- Gerwyn Price P 3 W 1 L 2 Leg Diff +-1
- Bradley Brooks P 3 W 0 L 3 Leg Diff -11
Group 32 - Monday May 18
- Peter Wright v Adam Hunt
- Krzysztof Ratajski v Justin Pipe
- Adam Hunt v Justin Pipe
- Peter Wright v Krzysztof Ratajski
- Krzysztof Ratajski v Adam Hunt
- Justin Pipe v Peter Wright
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