Arsenal's confidence grew but were dealt a hammer blow when the Toffees drew level.
Last weekend's goalscorers, Karoline Olesen and Snoeijs combining as the former played a perfectly weighted pass for the Dutch forward who broke through on goal.
With only Manuela Zinsberger to beat, Snoeijs calmly tucked the ball into the far corner on 24 minutes for her first league goal of the season.
The equalising effort appeared to inspire the visiting side as they grew more into Saturday afternoon's encounter.
Everton competed well with the hosts, but were dealt a cruel setback as Arsenal regained their lead five minutes into stoppage time in the opening half.
Lia Walti's inviting delivery was headed home by Mead past Brosnan.
Everton coped well in the second half against a dominant Arsenal but were unable to break the Gunners defence in a harsh outcome on Sorensen's side.
The Blues go again with a double-header against Leicester City next week. The Foxes hosting Everton in the League Cup on Wednesday evening followed by the reverse fixture in the Women's Super League on Sunday afternoon