Keith Bertschin's side included two England U19 international trialists in centre forward Mark Smythe from Liverpool and centre-back Pat Collins from Sunderland.
Dean Curtis had two good opportunities to give Bues the lead before Everton full back Daniel Fox scored the only goal of the game from a free kick just a minute before the half-time interval at Southport FC's Haig Avenue ground.
Curtis again had Blues best chance in the second half but his shot on 58 minutes was well saved by Everton keeper Richard Wright.
Everton: R Wright, Wynne, Fox, Hughes, S Wright, Schumacher, Fowler (Harris, 67), B Moogan, Booth, Pascucci (Anichebe, 72), Vaughan. Subs not used: Lake, Hopkins, Wilson.
Blues: Bennett, Parratt, Painter, Kilkenny, Courtney, Collins, Birley, Hall, Smythe (Hamilton, 45), Curtis, Motteram. Subs not used: Dormand, Howland, Blake.