The Blades were on top from the start, forcing three early corners inside the opening few minutes, but struggled to provide any clear chances until an in-swinging corner from Jodie Hutton was headed just wide of goal by Bex Raynor.
The initial threat made, Lewes immediately responded as Maria Farrugia charged up the pitch and slotted the ball into the net, the midfielder quickly called offside as the flag went up to keep the stalemate in place.
Continuing to pile on the pressure, it was a bustling few minutes for the Blades as Rayner went back on the attack, her curling effort held by shot-stopper Sophie Whitehouse just moments before Goodwin capitalised on a loose ball but saw her low effort pushed behind to keep it square at the break.
Chances were coming and going for the hosts as Whitehouse saved another opportunity on the hour mark, getting down to hold an effort from Ashley Hodson who was played in by a raucous Rayner.
Lewes produced their own sterling chance as a brilliant ball by Kate Oakley saw Farrugia's strike soar narrowly over the goal.
The deadlock finally ended on 73 minutes as Rachel Brown broke into the box and combined with Goodwin who slotted the ball in at the near post to take her team ahead.
A late surge from Goodwin almost doubled the lead but Whitehouse was once again to the rescue and the Blades were forced to settle with a 1-0 victory.
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