Lauren James and Jess Sigsworth had the best chances in a fiercely fought contest, with the visitors’ goalkeeper, Hannah Reid, producing a number of fine saves to keep United at bay in what is the Reds' first draw of the league campaign.
Casey Stoney made three changes from last weekend’s away victory against London Bees, with Jess Sigsworth, Ella Toone and Martha Harris all returning to the starting XI.
James, who celebrated her seventeenth birthday on Saturday, was the player that caused Durham’s defence the most trouble during a fairly even first half. The youngster had a golden opportunity to put the Reds into the lead early on after a delicious cross into the box by Greenwood which was pulled back across by Lizzie Arnot.