It was the cutting edge displayed by the visitors that made the difference with Simone Magill’s goal on the stroke of half-time a telling blow.
Blues had moments of promise early in the second half but Nicoline Sorensen added the second on the hour and substitute Valerie Gauvin sealed the deal late on.
Manager Carla Ward made two changes from Sunday’s quarter-final at Brighton, Gemma Lawley and Emma Kelly coming in for Georgia Brougham, ineligible due to her loan from Everton, and Abbi Grant.
Blues started brightly and went close in the sixth minute, Lucy Whipp’s cross into a busy box finding Harriet Scott at the near post but her headed effort looped into the grasp of keeper Sandy MacIver.
At the other end, Lucy Graham hooked towards goal following a scrappy set piece but Whipp was on hand to clear comfortably enough from in front of the line.
Graham then headed back across goal from a deep Everton corner for Rikke Sevecke to hit the bar from her station at the near post 17 minutes in.
Danielle Turner’s low centre just evaded Magill with Graham charged down at close quarters on the follow up as the pressure steadily built on Blues.
The breakthrough came a minute before the interval when a flick on the move from Izzy Christiansen played Magill down the right of the box to rifle into the roof of the net despite a strong offside appeal.
Blues continued to graft in search of an equaliser, Whipp taking a swing at a half volley that was smothered by MacIver low to her left seven minutes after the restart, while Claudia Walker’s shot on the turn despite being closely marshalled dropped agonisingly over having taken a deflection.
Optimism was punctured when a well-crafted move doubled the deficit on the hour, Megan Finnigan lifting over the backline to find the run of Ingrid Moe Wold and her cross was slammed into the empty net by Sorensen at the far post.
There were few openings from there but Everton made absolutely certain of progress when Gauvin’s well-timed run was followed by a finish across goal two minutes from the end.
Blues: Hampton, Scott, Lawley, Corsie, Holloway, Corsie, Whipp (Scofield, 64), Mayling, Green, Kelly (Grant, 64), Walker.
Unused subs: McCarron, Napier, Toussaint.
Yellow cards: Scott 29, Murray 69.
Everton: Maciver, Moe Wold, Finnigan, Sevecke, Turner, Clemaron (Pike, 74), Christiansen (Stringer, 90+1), Sorensen (Raso, 66), Graham (Egurrola, 90+1), Boye-Hlorkah, Magill (Gauvin, 74).
Unused subs: Egurrola, Stringer, Pattinson, Korpela (g/k).
Goals: Magill 44, Sorensen 60, Gauvin 88.
Referee: Amy Fearn.