Ashley Hodson opened the scoring for the Reds but Celtic levelled through an excellent strike from Charlie Wellings.
Melissa Lawley then edged Liverpool FC Women back in front before summer recruit Rianna Dean made it 3-1.
Jodie Bartle pulled a late goal back for the visitors following a corner but the Reds held on for the victory.
It was an excellent work out for Matt Beard's side and Rachel Furness stepped up her fitness by getting some more valuable minutes under her belt.
Liverpool FC Women played out a competitive 2-2 draw with Manchester United Women at Carrington on Sunday.