A late goal denied the Reds a victory to kick off their FA Women's Championship campaign against Durham on the opening day.
But Vicky Jepson's side bounced back in clinical fashion and produced a fine attacking display at The Hive in their second outing.
Melissa Lawley put Liverpool into the lead before a brilliant solo effort from Rinsola Babajide made it 2-0.
And Furness added further gloss to the scoreline with a third goal at the end of the game, her second in as many matches so far this term.
"First and foremost, it was a great reaction from last weekend against Durham," she reflected post-match.