Scott Rogers’ side moved level on points with third-placed Reading, and Arsenal one spot further back, by virtue of the result at the Swansway Chester Stadium.
The Reds capitalised on an encouraging start to a contest with connotations for the top and middle of the division by notching its only goal through England with just 10 minutes on the clock.
Alex Greenwood’s short corner routine with Caroline Weir opened up the chance to trouble City with a cross from the left side and the determined Liverpool striker was first to the ball with a clinical header at the near post.