Longhurst struck in the 11th minute as the Reds claimed their first FA Women’s Super League win since the first day of the season while bottom of the table Everton slumped to their fourth defeat in six.
Everton made the brighter start and almost took the lead inside two minutes but Libby Stout produced a brilliant save to keep out a close range effort from Nikita Parris.
And Everton then found themselves behind when Corina Schroder made progress down the left and crossed to Natsha Dowie, whose lay-off was superbly side-footed into the net from distance by Longhurst.
Dowie almost doubled the advantage but her header from a Fara Williams free-kick was just wide of the post.
Everton pressed forward after the break and Stout did well to prevent an own goal from Schroder, who had deflected a Lindsay Johnson cross.
Moments later, Longhurst had a great chance to score her second goal of the evening but she slipped somewhat and shot over the bar.
And there was further drama late on, Gemma Davison almost wrapping up the victory for Liverpool, only to be foiled by a brilliant save from Rachel Brown-Finnis, before Parris shot wide from close range at the other end when given an opportunity to bag a late equaliser.
Liverpool manager Matt Beard said: “It was a typical derby.
“I have to give Everton credit because it was a fantastic match to be involved in, very hard-fought.
“The league is really tight and there are a lot more quality teams now.”
Elsewhere, Yuki Ogimi and Ji So-Yun were on target for Chelsea as they beat Arsenal 2-1 in a London derby.
Ogimi opened the scoring with a great goal after 49 minutes, expertly chipping the ball over Emma Byrne from the edge of the box after latching on to an Eniola Aluko pass.
The goal scorer was then body checked on the edge of the box after 63 minutes by Niamh Fahey and So-Yun stepped up to curl a delightful free-kick around the wall and into the net.
Kelly Smith pulled one back two minutes later, converting a penalty after a handball from a corner, but Chelsea held on for the win despite the late dismissal of Gilly Flaherty, who picked up her second yellow card in stoppage-time for dissent.
At Damson Park, Emily Westwood scored the key goal as Birmingham avenged last Sunday’s 5-0 FA WSL Continental Cup loss to Bristol Academy with a 2-1 win over the same opponents.
The league leaders took the lead after 11 minutes when Karen Carney found the top corner with a superb free-kick.
And they doubled the lead ten minutes after the break, Jo Potter drawing the goalkeeper before setting up an easy finish for makeshift striker Westwood, who normally plays at centre-back.
Bristol pulled one back when a Laura del Rio free-kick was flicked into her own net by Hannah George but they could not manage an equaliser.