Sheffield United remain mired in relegation danger as Aston Villa took full advantage of some poor defending.
Ashley Young scored Villa's second goal
Gabriel Agbonlahor gave Villa the lead after he got away from Matthew Kilgallon before powering an unstoppable shot past Paddy Kenny.
Chris Montgomery was the next United defender to be embarrassed by Villa's speed when he was tricked by Ashley Young, who beat Kenny with a low shot.
Patrik Berger made and scored Villa's third to add to United's discomfort.
This defeat leaves United probably needing points from their their final game of the season against Wigan at Bramall Lane to be certain of Premiership survival.
United have only won three away league games and Neil Warnock's side never really appeared capable of improving on that record.
For the start of the second half Warnock made two substitutions, introducing Mikele Leigertwood and Luton Shelton.
Briefly United hinted the game might not be over and Chris Morgan went close with a shot.
But Berger's cleverly constructed goal effectively ended United's interest in the match.
A quick exchange of passes with Carew allowed Berger the time and space to beat Kenny with precisely-placed shot.
Had Kenny not made important saves to deny Martin Laursen and Craig Gardner, United's defeat might have been even more costly given that their goal difference is now only one better than Wigan.
Kenny's frustration at the lack of protection he had been offered was evident when he angrily threw the ball at Kilgallon, sparking a heated row between the keeper and his defender.
In a disastrous opening first-half for United, Agbonlahor, Young and Carew were just too quick for the visitors.
In the opening minute Carew outsprinted the United defence and soon after went one better in getting in a shot.
Midway through the first half Agbonlahor wriggled clear of Kilgallon and unleashed a rising left-footed shot past Kenny.
Soon after Agbonlahor might have had a second, when he weaved his way into a shooting position, only to see his effort beaten away by Kenny.
Just before half time Young exposed United's ponderous defending for a second time, skipping past Montgomery and then arrowing a low shot past Kenny.
Aston Villa manager Martin O'Neill on the inspiration provided by the parade of the club's 1982 European Cup winning before the match:
"The appearance of the 1982 team gave us a lift.
"They've shown us the way - those were heady days for the Villa.
"We were deserved winners. It was great to play well and win at home as we haven't done that enough this season.
"This is a day for celebration, but we've got miles to go."
Sheff Utd Neil Warnock:
"We've a home game to come and it's still in our hands and that's the way we want it to be.
"We were poor, but we were beaten by a super team - they were exceptional and we just couldn't cope with them.
"The players' heads are down at the moment, but I've been so proud of them this season - they've worked so hard."
Aston Villa: Sorensen, Hughes, Mellberg, Laursen, Bouma, Agbonlahor (McCann 83), Gardner, Barry, Berger (Davis 72), Carew (Moore 79), Young.
Subs Not Used: Taylor, Cahill.
Booked: Barry, Mellberg.
Goals: Agbonlahor 25, Young 42, Berger 59.
Sheff Utd: Kenny, Geary, Morgan, Kilgallon, Armstrong (Shelton 46), Gillespie, Montgomery (Leigertwood 46), Jagielka, Tonge, Kazim-Richards, Stead (Webber 85).
Subs Not Used: Davis, Alan Quinn.
Booked: Leigertwood, Kenny.
Ref: P Walton (Northamptonshire).