Two months ago the Toffees were humiliated at Goodison Park when the Gunners trounced them 6-1 and, although the Merseysiders have improved since then, defensive frailties were again to the fore as they slipped to another embarrassing loss in Portugal.
Everton are still likely to qualify for the next stage of Europe's secondary competition after beating AEK Athens and BATE Borisov in their first two group games, but the team's threadbare defence must surely be concerning Moyes.
With Leighton Baines joining the lengthy injury list at Goodison, Moyes was forced to field Seamus Coleman in his place and the youngster was unable to cut out the cross that led to the opening goal in the 14th minute.
The outstanding Angel Di Maria's deep ball into the area found Javier Saviola who volleyed the ball into the ground and over Tim Howard to give Benfica the lead.
Everton seemed to lack creativity with most of their half-chances in the first period coming from set-pieces but their predicament was to deteriorate significantly after the interval.
The Stadium of Light crowd celebrated three goals in five minutes as the Portuguese side showed their class.
First Di Maria dispossessed Maroune Fellaini and crossed for Oscar Cardozo who had the simple task of tapping the ball home before the same combination made it 3-0.
This time Cardozo was on hand to head Di Maria's cross into the net and it was game over.
Before Everton could gather their thoughts they conceded a fourth goal when Pablo Aimar's corner found the unmarked Luisao whose header beat Howard after coming off the far post.
It almost immediately got worse for the Premier League side as Di Maria crashed a shot against the crossbar and only a superb Howard shot stopped Cardozo from completing his hat-trick.
After Louis Saha had hit a post, Benfica grabbed their fifth goal in the closing stages when Di Maria once again cut the Everton defence to shreds before crossing for Saviola to turn the ball home from close range.