Heath's stunning strike got her side back into the game before substitute Kirsty Hanson equalised 20 minutes from time at the Leigh Sports Village.
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City dominated the first half and deservedly scored two goals through Chloe Kelly and Laura Coombs. However, the FA Cup winners struggled after the break and United produced an impressive second half display to earn a point.
United remain at the top of the Women's Super League while City remain in fifth place.