The FA Women's Championship clash was settled by a header from the Reds captain midway through the second half.
Substitute Missy Bo Kearns sent in a trademark delivery from a corner and Fahey was on hand to guide in what proved to be the winner.
The result made it back-to-back victories for interim manager Amber Whiteley and successive clean sheets, too.
"I'm just massively happy to get the three points," said Fahey.
"It was a tough game, it could have gone either way really but we played some good stuff away from home so we are happy.