Brazilian Wesley scored his first goal for Villa after Jota's excellent pass put him clean through before finding the bottom corner.
Dominic Calvert-Lewin had a fine chance to level 10 minutes after going behind but Bjorn Engles blocked his goal-bound effort on the line.
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Much like the first half, Everton had more of the ball but failed to create any real clear cut opportunities in the second until late on. Alex Iwobi, making his debut for Everton struck the post in the closing stages.
Theo Walcott should have equalised for Everton in the final minute of the match, but somehow put Moise Kean's cutback over the crossbar from six yards out with Tom Heaton nowhere to be seen.
Anwar El Ghazi secured Villa’s first win in the Premier League since February 2016 in the fifth and final minute of injury time after a quick counter attack.
Dean Smith's side move up to 11th in the table, while Everton who conceded their first goals of the season remain in ninth before the rest of the weekend’s action.
Aston Villa pick up first points fo the season
Everton were dominant in the opening exchanges of the match but were left stunned in the 21st minute when Villa opened the scoring with their first chance of the game,
Jack Grealish's quick free-kick allowed Jota to skip away and his superb throughball found Wesley to fire across Jordan Pickford.
With something to cling to Villa grew in confidence and Yerry Mina's last-ditch challenge was needed to thwart Wesley three minutes after his opener.
Everton's grip on the game, however weak, had been lost but they should have levelled after 32 in the 32nd minute.
Morgan Schneiderlin set Seamus Coleman free and his cross fell to Calvert-Lewin but his casual finish was blocked on the line by debutant Engels.
It was the only serious first-half threat the Toffees created though and Villa began to feel more settled in their Premier League skin.
As Villa stood firm Everton waned, Mina headed over Lucas Digne's corner early in the second half but Everton were floundering, lacking direction and purpose.
Moise Kean and Iwobi were summoned from the bench as Marco Silva threw caution to the wind.
Everton had spent most of the second half probing for a leveller and they came agonisingly close to equalising with eight minutes left when Iwobi latched onto Michael Keane's knockdown and his effort hit the base of the post.
El Ghazi tested Pickford from distance soon after yet Walcott should have levelled in the 89th minute but volleyed over from six yards after being picked out by Kean.
El Ghazi then rolled in to seal the points for Villa in stoppage time after being teed up by John McGinn.
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