Injuries have ravaged the squad so Neill is a welcome addition after his contract expired at Upton Park and he became a free agent.
With three defeats in their opening Barclays Premier League campaign, Everton were looking for boost outside of domestic competition.
Moyes need not have worried as his side were in control from the start in this Europa League match with Joseph Yobo, Sylvain Distin and Steven Pienaar all scoring before half time. Jo added a fourth in the second half.
However, the night ended on a sour note with substitute Louis Saha sent off in stoppage time for lashing out at Juanfran.
Russian midfielder Diniyar Bilyaletdinov marked his first start by having a hand in the first three and was given a rousing reception when he came off in the second half.
AEK were on the back foot after only seven minutes when Pienaar tried to release Jo only for Sanel Jahic to make a timely interception.
It was a taste of what was to come as Pienaar came within inches of putting Everton ahead two minutes later with a fierce shot.
Goalkeeper Sebastian Saja parried his effort around the post. Bilyaletdinov delivered the corner and Yobo peeled away from his marker to open the scoring.
Everton went 2-0 ahead in the 17th minute and it was another corner from the Russian that led to the goal.
The Greek side failed to deal with it and Marouane Fellaini was the first to react in a crowded area.
Even though he failed to get a decent touch, AEK were all at sea and the ball broke to Distin, who made no mistake from close range.
Jo came close to extending their lead in the 24th minute, heading narrowly over the bar from close range.
The Brazilian was then first to react when the ball was pumped into the area but found the wrong side of the post with his close-range effort.
Bilyaletdinov then came close in the 35th minute after good link-up play involving Pienaar and Jo.
Everton were cruising and Pienaar made it 3-0 in the 37th minute with a goal out of nothing.
The South African latched on to a good crossfield ball from Bilyaletdinov to thump a shot from 25 yards beyond the goalkeeper.
AEK's troubles increased in the 55th minute with Carlos Araujo sent off after kicking out at Distin following a challenge with the French defender.
Everton were prepared to play with patience in a bid to extend their lead.
Substitute Ayegbeni Yakubu laid the ball into the path of Pienaar in the 62nd minute only for the goalkeeper to stick out a hand and parry his effort from 20 yards.
Then Jack Rodwell tried his luck from distance but Saja made a comfortable save.
Everton kept up the pressure and Leon Osman clipped a shot wide of the post in the 66th minute after Yakubu had carved out the opening for the home side.
Saha should have extended their lead in the 79th minute but sent his shot over the bar from four yards.
But they did not have long to wait with Jo getting their fourth goal three minutes later before Saha's sending off.