Yet the Toffees suffered another defeat that stretched their wretched form in the Premier League to just one win in 14 matches.
The first half proved a tight affair but Villa took the lead in stoppage-time.
Lucas Digne - who left Everton for the midlands club earlier this month - whipped in a corner and Emi Buendia glanced home a header at the front post.
The Toffees thought they had an equaliser in the 61st minute through Ben Godfrey but visiting skipper Tyrone Mings made a crucial block off the line.
The hosts continued to push for a leveller but failed to test Emi Martinez in the Villa goal.
Now the search continues for Everton to find their next manager as fears of being dragged into a relegation battle grow.
- Emi Buendia: the Argentine was Villa’s chief attacking threat throughout. In the first half, he stung the palms of Jordan Pickford with a low drive after fine work. And despite being a diminutive figure, he was there to latch on to Digne’s corner and get enough purchase on his header to deliver his side three points.
- Tyrone Mings: a match-winning goalline clearance. Mings might have been in the right place at the right time but had he not been, Godfrey would have equalised.
- Anthony Gordon: the Everton substitute pepped his side up when coming on for Andros Townsend. It was his corner that led to Godfrey’s chance while he put a cross into the box that Dominic Calvert-Lewin should have converted.
- Dominic Calvert-Lewin: the striker’s effort or application could not be fauled all game. He gave the Villa defence problems in the air. But when his big chance arrived in the 65th minute, Calvert-Lewin was unable to remain composure and saw is effort go over.
- Yerry Mina: spurned two big headed opportunities in the second half, failing to get the target. Also got caught over the top on a couple of occasions in the first period.
- Craig Pawson: the referee didn’t let the game flow throughout. Very stop-start and struggled to stamp his authority.
Everton: Pickford 6, Kenny 5, Mina 5, Holgate 5, Godfrey 5, Townsend 5 (Gordon 56; 7), Doucoure 7 (Onyango 65; 5), Gomes 5 (Allan 51; 5 ), Gray 5, Richarlison 6, Calvert-Lewin 6.
Aston Villa: Martinez 6, Cash 6, Consa 6, Mings 6, Digne 6, Ramsey 7, McGinn 6, Luiz 6 Coutinho 5 (Chukwuemeka 74; 5), Buendia 7 (Hause 91), Watkins 6 (Ings 79).
What’s Everton’s next fixture
The Blues now have a two-week break before they are next in action.
They host Brentford in the FA Cup fourth round and there could well be a new manager in charge by then.