The Villans beat Crystal Palace on Sunday to remain within four points of safety with three games to go, while Everton are stuck in mid-table following defeat to Wolverhampton Wanderers.
The pressure was on Villa heading into their clash with Crystal Palace at the weekend after seeing West Ham United and Watford pick up victories on Saturday.
A first league win since January 21 - secured thanks to a couple of goals from flop winger Trezeguet - ensures that the Villans have hope of beating the drop.
For that to happen, though, they will have to match that performance against Everton, another side who - just like Palace - have very little to play for on the face of it.
Indeed, Toffees boss Carlo Ancelotti admitted as much on the back on Sunday's 3-0 reverse at the hands of Wolves, a result that leaves the Merseyside outfit 11th in the table.
Everton are winless in three matches and are now 10 points off sixth-placed Wolves, meaning that Europa League qualification is out of the question.
Ancelotti will at least take solace from his side's home form, with Everton unbeaten at Goodison Park in the league since the end of November.
That 10-game unbeaten home streak is Everton's best since December 2016 and second only to city rivals Liverpool in terms of ongoing runs.
Coming away from Goodison Park with all three points will be a massive ask for Villa, then, but with Arsenal up next that has to be the target on Thursday evening.
However, not since 2001-01 have Villa secured a league double over Everton, and they have lost each of their last three meetings at Goodison Park.
After ending a 10-game wait for a victory last time out, Smith's side now need to make it back-to-back wins for the first time since October to remain on course for a great escape.
Everton's Premier League form: DWWLDL
Aston Villa's Premier League form: LDLLLW
If not, youngster Jarrad Branthwaite is in line for a full Premier League debut in what will likely be a four-man defence.
Everton possible starting lineup:
Pickford; Sidibe, Holgate, Keane, Digne; Iwobi, Davies, Gomes, Gordon; Richarlison, Calvert-Lewin
Aston Villa possible starting lineup:
Reina; Elmohamady, Konsa, Mings, Targett; McGinn, Luiz, Hourihane; Trezeguet, Davis, Grealish
We say: Everton 2-0 Aston Villa
This is a game Villa must realistically take three points from to keep their survival hopes intact. Everton may have little to play for, but they have a good home record this season and will be desperate to bounce back following a recent slump in form.