Greaves is making her tournament debut and hit three 180s on her way to victory over the Dutchwoman at the O2.
She will now face last year's champion Mikuru Suzuki after she beat Russia's Anastasia Dobromyslova in the last women's match of the night session.
2020 BDO World Championship
Suzuki defeats Ashton in women’s BDO final whitewash
11/01/2020 AT 22:52
Corrine Hammond beat Laura Turner 2-0 in the other women's quarter-final match in the early session.
She will face Lisa Ashton for a place in the final after the top seed beat Lorraine Winstanley 2-0 in the first of the evening games.
In the men's side of the tournament second seed Jim Williams made short work of Ryan Hogarth, hammering his opponent 4-0 on his way through to the quarter-finals.
Meanwhile in first evening game for the men Mario Vandenbogaerde hammered Dennie Olde Kalter 4-1.
2020 BDO World Championship
Williams to meet Warren in all-Welsh BDO World final
11/01/2020 AT 17:25
2020 BDO World Championship
'Why oh why would you do that??' - Warren punished for big gaffe
11/01/2020 AT 17:02