Five shots on target in the opening half yielded five goals for Emma Hayes’ side, with Guro Reiten putting the hosts ahead after 12 minutes.
Sam Kerr made it two with a powerful header before injury saw her evening end early. Her replacement Pernille Harder made it three before Jessie Fleming added a fourth.
On the stroke of half time, Fleming scored her second of the game to make it five.
Everton improved after the restart but offered little to reduce the deficit.
And it was the hosts who found the net again on 81 minutes; Harder’s first-time finish evaded Courtney Brosnan for her second goal of the game.
Erin Cuthbert completed the scoring in injury time, as Everton endured a game to forget in the capital.
Speaking after the final whistle, coach Brian Sorensen expressed bemusement about how quickly the game turned for his side, but tried to keep a brave face with little to play for in the remaining three games of the season.