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