Vicky Jepson’s Reds had equalised an early concession through Jessica Clarke at Merseyrail Community Stadium but could not produce a second leveller, with Leandra Little hitting the post late on.
The visitors fell behind in the fifth minute as Inessa Kaagman found the top corner with a perfectly-placed thump from 25 yards out.
They produced a quick response, however, in the 12th minute.
Everton goalkeeper Kirstie Levell made an outstanding save to block a close-range shot after a short corner routine by the Reds – but Clarke was on hand to tap home the rebound.
The Blues restored their lead shortly before the interval, though, courtesy of another long-range strike.