Scott Rogers' charges were full value for their win as they gained three valuable points in the Women's Super League.
In a fairly even opening 45 minutes both sides had their chances. Siobhan Chamberlain made a brilliant stop for the Reds while at the other end of the field Jess Clarke and Caroline Weir both went close.
The breakthrough arrived three minutes into the second half and England fired Liverpool Ladies into the lead with a superb volley.
Laura Coombs then drove just wide and Weir went close as the Reds looked to increase their tally.
Rogers' side had to wait until five minutes from time to double their advantage and it came from the penalty spot. England was brought down and Greenwood cooly slotted home the second goal.
Liverpool Ladies: Chamberlain, Murray, Greenwood, Longhurst, Bonner, Ingle, Hodson (Harris, 86), Coombs (Rodgers, 88), Clarke (Johnson, 18), Weir, England.