Rovers had won four and drawn one of their previous last five league and cup games at Ewood Park and created a clutch of chances in the opening period.
Carson, pilloried in the press after his disastrous showing for England last Wednesday, soon showed the kind of form sadly absent against Croatia.
He first denied David Dunn from 25 yards, tipping the ball out for a corner, then Nelsen from 20 yards before saving David Bentley's curling free-kick.
Roque Santa Cruz shot wide and later passed for Benni McCarthy to slot home only for a questionable offside flag to rule the goal out.
Having failed to capitalise on their impressive start, Rovers were punished when Carew struck - his glancing header from Young's free-kick leaving the advancing Brad Friedel stranded.
Villa threatened again before the break. Another Carew header, this time a flick-on from a long ball forward, played Agbonlahor through.
The Villa striker hooked the ball goalwards with his first touch but this time Friedel was equal to the task, blocking Agbonlahor's effort.
McCarthy might have restored parity within minutes of the restart but his crashing volley struck Wilfred Bouma on its way to goal.
And Villa scored the game's decisive second, doubling their advantage with the penalty that also resulted in the dismissal of Nelsen.
Nelsen did pull Agbonlahor's shirt but contact was minimal and the red card decision seemed unnecessary after referee Phil Dowd had already pointed to the penalty spot.
The excellent Barry, striking the ball low into the corner, eluded Friedel's dive.
Ten-man Rovers were left with 38 minutes to try to salvage something from the contest and pushed forward whenever possible.
But Villa eventually made their numerical advantage tell through Young, who superbly finished from 20 yards.
The chance appeared to have gone when Agbonlahor's pull-back initially failed to pick out a Villa player but the ball rolled all the way out to the winger, who closed in on goal before shooting.
Harewood scored his 100th league goal close to the final whistle after Friedel had parried Carew's initial strike.
The ball looped up and fell to the unmarked Harewood, who had plenty of time to compose himself before striking the fourth.
Blackburn boss Mark Hughes:
"We have been beaten 4-0 but no way was there four goals between the teams.
"For the first 30 minutes we were totally in control of the game.
"The turning point was the penalty. It was a penalty but why the referee sent him off, you'll have to ask him that."
Aston Villa boss Martin O'Neill:
"It has been a terrific effort in the last few weeks.
"I think the game was closer than the scoreline suggests but I think we defended very strongly and Gareth Barry is back to his very, very best.
"I was concerned about the game beforehand. That was our game in hand and we have won it."
Blackburn:
Friedel, Ooijer, Samba, Nelsen, Warnock, Emerton,
Mokoena (Reid 67), Dunn, Bentley (Pedersen 81), Santa Cruz,
McCarthy (Roberts 67).
Subs Not Used: Brown, Savage.
Sent Off:
Nelsen (52).
Aston Villa:
Carson, Mellberg, Knight, Laursen, Bouma,
Petrov (Gardner 82), Reo-Coker, Barry, Young, Carew,
Agbonlahor (Harewood 85).
Subs Not Used: Taylor, Davies, Berger.
Booked:
Mellberg.
Goals:
Carew 29, Barry 53 pen, Young 81, Harewood 89.
Att:
20,776
Ref:
Phil Dowd (Staffordshire).
