Fielding a team short of six regulars due to injuries and non-availability, the Millers started this FA Cup clash in Merseyside the better and earned an early goal lead from Hayley Wood after fine work from Charlotte Spencer.
The young Rotherham team looked in control of the game until midway through the first half when a defensive error gave the Liverpool forward a chance to equalise and she did so with ease.
Liverpool had a lot of possession for the remainder of the half but the Rotherham defence coped admirably with whatever was thrown at them.
Hayley Wood should have taken the visitors into the half time break after rounding the 'keeper but she allowed the Liverpool defender to clear.
The second half saw the home side control most of the play and they scored 15 minutes into the half direct from a 20 yard free kick, after a silly hand ball by Sarah Saxon who caught the ball after saying "she heard the whistle" but the referee was having nothing to do with her comments.
The home side scored their third 15 minutes from time after the Rotherham defence was caught napping but in fairness to the Liverpool forward, she very calmly converted her chance so Liverpool took a 3-1 lead.
After loosing Hayley Wood to a re-occurrence of her hamstring problem that kept her out for three weeks, Helen Lynskey was pushed up front for the last 10 minutes and she was rewarded with a fine strike near the end.
Liverpool held out for the last few minutes and deservedly went through to the next round.
All the Rotherham players were commended by their manager for their effort but it wasn't quite enough on the day.
