The pair had a frosty time on stage, with Price not willing to engage nicely with Wright.
When Wright tried to have a bit of a laugh with Price after winning the opening set, Price did a strange lunge as Wright walked past.
"He wasn't having a joke downstairs not have one on the stage, it's not my problem," Wright said.
Wright also said: "Before the match me and Gezzy were winding each other up. I like Gezzy but I don't appreciate what he's done. He wanted me to concentrate? I concentrated. There you go. You lost.
"It spurred me on because it wound me up. If you wind me up on the dart board I'll get you back."
The highly rated Wright, who has a long history of struggling to actually win titles, will play Dutch darts supremo Michael van Gerwen in Thursday morning's final.
Van Gerwen was unconvincing in beating England's Nathan Aspinall 6 - 3 as he seeks his fourth world crown.