Sherrock sent the clash to a deciding leg, but 22-year-old Greaves held her nerve with 54 remaining to take the spoils for a record third time.
It is the second time the pair met in the Women's World Matchplay final, with Greaves also coming out on top 6-3 in 2024.
"I'm not one to celebrate, but I just felt the relief after winning," Greaves told Sky Sports.
"To hit that last dart was just an outpouring of relief. I am just so happy to win.
"I was nervous. That kind of pressure is a privilege - I am doing well and playing well. I didn't think I played my A-game, but just to win and get over it is such a massive thing. It is a terrific night."
Greaves was the favourite heading into the match after cruising through her quarter-final, although she was then pushed by Gemma Hayter.
Like Sherrock, Hayter forced their tie into a decider, where Greaves produced a magical 104 checkout to progress.
Sherrock, meanwhile, fell short in the final for the third year in a row and was in good form on the day in the lead-up.
She dropped just one leg across both her matches, which came as she defeated the reigning champion Lisa Ashton 5-1.