An early own goal and a header from Meikayla Moore after the interval made the difference for the Reds at a sun-drenched Prenton Park.
Interim manager Amber Whiteley’s side started the contest with real purpose and could have had a couple of goals within five minutes.
First, a fine team move ended with Kirsty Linnett shooting on goal but Tatiana Saunders was well behind it in the Lewes’ net.
Linnett next turned provider to set up Ceri Holland, who was denied by a last-gasp block, before Linnett’s own effort from close range was deflected just wide.