The Villans returned to winning ways at Leeds United last time out and are six points off the Champions League spots with two games in hand.
Sheff United were beaten 2-0 by Liverpool, meanwhile, and are now 15 points adrift of safety with just 12 more games left to play.
A run of three wins in five games gave United a glimmer of hope of survival, but four defeats in a row since then has left even boss Chris Wilder accepting his side's fate.
Indeed, the Blades have failed to even score in the last three of those losses to West Ham United, Fulham and Liverpool.
That was the Blades' 10th home league loss of the campaign, which is just one short of their all-time record of 11 set in the Championship a decade ago.
Wilder admitted that his side "lacked quality and strength in depth" against the Reds, which he will attempt to address over the summer - assuming the Yorkshireman is still in charge.
While United are the worst side in the division in terms of home form - and indeed overall - opponents Villa have taken 23 points from 13 away matches this campaign.
That is a figure bettered only by Everton, Manchester United, Leicester City and Manchester City, the most recent of their away wins coming at Elland Road on Saturday.
Anwar El Ghazi settled the match with an early strike to earn Villa a first win in three, having lost to Leicester and drawn against Brighton and Hove Albion in their previous two.
However, since winning their first four Premier League games this season, Dean Smith's men have won back-to-back matches just once since then.
If they are to keep pace with the big hitters in the battle for Champions League football, they will have to put that right at Bramall Lane on Wednesday evening.
Sheffield United Premier League form: WLWLLL
Aston Villa Premier League form: WLWDLW
As for Villa, Jack Grealish remains a major fitness doubt after missing their last two matches - though his absence was not felt as much as some predicted in the win against Leeds.
Sheffield United possible starting lineup:
Ramsdale; Ampadu, Jagielka, Bryan; Baldock, Lundstram, Norwood, Fleck, Stevens; Mousset, Sharp
Aston Villa possible starting lineup:
Martinez; Elmohamady, Konsa, Mings, Targett; Luiz, McGinn; Traore, Barkley, El Ghazi; Watkins
We say: Sheffield United 0-2 Aston Villa
Villa have enjoyed an impressive campaign and still have plenty to play for, whereas Sheffield United now seem to have accepted the inevitable.
The Blades have won just three times all season and we cannot see that figure improving on Wednesday against a Villa side back to winning ways.
Watch the Sports Mole Football Shorts prediction for this game below: