The world number four joins Martin Lukeman in the next round of the competition - who he lost to earlier in the group stages.
Cross needed a win against Wright to advance following the defeat to Lukeman and a victory over Leonard Gates, which he delivered in dominant fashion.
"I was playing a legend of the game," the Englishman said of his iconic opponent Wright.
"Peter’s not at his best. He’s a two-time World Champion, he’s a great man and he’s given a lot to the game. I hope he can come back. I hope he can rebuild.
"I wasn’t at my best tonight, but it’s great to be through. It’s a longer format now so I can relax a little bit, and I’ll be ready to go on Wednesday."
Cross is next in action in the knockout rounds against Ritchie Edhouse, who he has already beaten once - and lost to twice - this year.