On the hour mark Darren Potter sent a free kick to the back post were Anderson was waiting and he connected with an unstoppable half volley to win the game for the Reds.
Liverpool gave a game to MK Dons trialist David Martin and while the 19 year old goalkeeper did keep a clean sheet, in all honesty he had nothing to do thanks to good performances from Godwin Antwi and Miki Roque.
Antonio Barragan continued his recovery from injury with another 90 minute run out, this time at right-back.