Manager Marc Skinner awarded first starts to summer signings Geyse and Gabby George for the curtain-raiser, but it was super sub Williams who bagged the winning goal.
After a first half which saw chances from both sides, it took until nearly 80 minutes to get a goal at Villa Park.
Rachel Daly slotted the ball past Mary Earps to score for the hosts, moments after former Red Kirsty Hanson had been dismissed for a dangerous challenge, before Lucia Garcia levelled the score for United.
It looked like the sides were set to share the points but Nikita Parris found Williams in the box and she headed it in to clinch the victory for the Reds.