Ollie Watkins led the line for Unai Emery and though his squandered the chance to embarrass Jordan Pickford in the first had after the goalkeeper found himself stranded, he punished his England teammate early in the second half, reminding fans of his quality in the final third.
The Toffees' lack of threat was on full display, with Villa holding onto the lead and keeping their first clean sheet in their last eight games.
The result leaves Everton in 16th place with 17 points, and they are only one point above 18th-placed Wolverhampton Wanderers.
Meanwhile, Villa are seventh with 35 points and are level on points with sixth-placed Manchester City, and are just three points from fourth-placed Newcastle United.
SPORTS MOLE'S VERDICT
The Toffees are set to move into their new stadium next season, but unless they significantly improve their offensive output, they could welcome fans to their new ground in the Championship.
Only last-placed Southampton have scored fewer than Everton's 15 league goals, and though their defence has proven to be resilient at times this season, it is difficult to see how Moyes can keep his side in the top flight without a drastic change in the final third.
Everton's opponents Villa will be delighted with the win and the three points means Emery has won his last three games in charge, and the visitors' Champions League hopes are well and truly alive.
EVERTON VS. ASTON VILLA HIGHLIGHTS
17th min: Ollie Watkins (Aston Villa) miss
Watkins races towards goal from the left flank with Everton goalkeeper Jordan Pickford in no man's land, but he strikes from the corner of the box and past the right post.
A huge chance missed!
Ollie Watkins goal vs. Everton (51st min, Everton 0-1 Aston Villa)
Moragn Rogers picks up a loose ball near the halfway line on the right, before threading a ball through to Watkins, who is clear through on goal on the left and he expertly slots a left-footed shot past Pickford.
His ninth Premier League goal of the season!
93rd min: Dominic Calvert-Lewin (Everton) miss
Pickford plays a long pass into Aston Villa's half, and Jesper Lindstrom latches onto the ball on the right of the box before he fins Dominic Calvert-Lewin free in the penalty, but the striker skies his effort.
He should have scored!
MAN OF THE MATCH - BOUBACAR KAMARA
Boubacar Kamara has endured an injury-plagued spell with Aston Villa, but he was formidable in midfield alongside Amadou Onana, protecting the defence and helping build attacks.
In fact, Kamara made nine passes into the final third - the most of any Villa player - and also won 10 duels while earning five fouls.
EVERTON VS. ASTON VILLA MATCH STATS
Possession: Everton 50%-50% Aston Villa
Shots: Everton 10-11 Aston Villa
Shots on target: Everton 3-3 Aston Villa
Corners: Everton 8-5 Aston Villa
Fouls: Everton 17-10 Aston Villa
BEST STATS
WHAT NEXT?
Everton's relegation battle continues on Sunday when they face Tottenham Hotspur at home, before taking on Brighton & Hove Albion on January 25.
As for Villa, they are set to play Mikel Arteta's Arsenal on Saturday at the Emirates, and Emery's side return to Champions League action on January 21 when they travel to take on Monaco.
Written by
Lewis Nolan