Greaves, the Women's World Matchplay champion, averaged almost 104 in defeat and had won their previous meeting at last year's World Youth Championship.
Littler, the world number one, is chasing a third successive title and will reach the knockout stage if he beats Niels Zonneveld in Group A on Monday.
"Beau was fantastic, but I'm happy with my performance, and I've still got a 100 per cent record in Wolverhampton," said Littler.
Nathan Aspinall recorded the highest televised average of his career, 111.68, in a 5-1 win over Maik Kuivenhoven in Group P that included back-to-back checkouts of 149 and 120.
Gian van Veen averaged 110.51 in beating debutant Carl Sneyd 5-2, while Luke Humphries averaged 105.7 in a 5-3 win over Paolo Nebrida.
Michael van Gerwen survived two match darts in the deciding leg to beat Henry Coates 5-4 in Group L, the 16th year in a row he has won his opening group game. Coates hit five 180s and took out 121 and 156.
Ross Smith, Jonny Clayton and Josh Rock all lost and return on Sunday. Smith, the European champion, went down 5-3 to Rusty-Jake Rodriguez in Group O, Clayton lost 5-4 to debutant Anton Ostlund in Group G and Tommy Morris averaged 100.33 in a 5-2 win over Rock in Group C.
Gerwyn Price beat Joe Hunt 5-3 despite a 170 checkout from his opponent, and James Wade averaged over 104 in a 5-1 win over Cam Crabtree at the start of his record-equalling 19th Grand Slam. Tom Sykes beat Luke Woodhouse 5-3 on his debut in Group J.
Stephen Bunting beat Raymond Smith 5-4 and Ryan Searle won the last two legs in 23 darts to edge Charlie Manby by the same score. Wessel Nijman beat Adam Sevada 5-1, while Jermaine Wattimena and Chris Dobey were 5-2 winners over Lisa Ashton and Jan Schmidt.
Day one results:
Tom Sykes 5-3 Luke Woodhouse (J)
Jermaine Wattimena 5-2 Lisa Ashton (B)
Stephen Bunting 5-4 Raymond Smith (D)
Ryan Searle 5-4 Charlie Manby (F)
Tommy Morris 5-2 Josh Rock (C)
Wessel Nijman 5-1 Adam Sevada (H)
Nathan Aspinall 5-1 Maik Kuivenhoven (P)
Anton Ostlund 5-4 Jonny Clayton (G)
Gerwyn Price 5-3 Joe Hunt (E)
James Wade 5-1 Cam Crabtree (K)
Rusty-Jake Rodriguez 5-3 Ross Smith (O)
Michael van Gerwen 5-4 Henry Coates (L)
Luke Humphries 5-3 Paolo Nebrida (I)
Luke Littler 5-2 Beau Greaves (A)
Gian van Veen 5-2 Carl Sneyd (M)
Chris Dobey 5-2 Jan Schmidt (N)