But with the game drifting and Villa looking lacklustre, a mistake from Carroll changed the course of the game.
Young swung an innocuous free-kick towards goal from 30 yards on 25 minutes and, as Olof Mellberg challenged him, Carroll failed to make any real contact to clear and the ball went straight into the net.
Cue Derby's catastrophic collapse.
Less than 60 seconds later, England midfielder Barry broke down the left wing to cross, Carroll could only push the ball away from a sea of bodies out to Carew, and Villa's big striker rammed a vicious shot back into the goal.
Jewell is still without a win in his 20 games as manager
With Derby's confidence now at rock bottom, Villa streamed forward in waves but it was another Carroll clanger which led to their third.
A routine punt downfield was skewed towards Petrov who, 45 yards from goal, controlled impeccably and then lashed back over Carroll's head into the top corner for a breathtaking goal.
That was enough for some Derby fans who have not tasted victory in 30 games and they soon filed towards the exit gates before half-time.
And the East Midlanders' suffering continued into the second-half.
On 53 minutes, Young neatly played England colleague Agbonlahor into the box and the rebound from his low shot, saved smartly by Carroll, was tapped home by Barry with Derby's defence at a complete standstill.
O'Neill offered Derby consolation
Derby plugged away and Robbie Earnshaw forced Carson into a flying save but the Rams agony continued on 75 minutes.
A simple clearance inadvertently knocked on by a Derby defender was pounced upon by Agbonlahor who tucked into the corner from 15 yards.
Five minutes before full-time Patrik Berger played in fellow substitute Harewood who raced beyond Derby's static defence to coolly slot home past the beleaguered Carroll and boost Villa's European hopes.
The only relief for Derby was the final whistle and they are now in danger of becoming only the second club ever in history to go through a full league season with just one win.
The Rams now stand on the brink of breaking a host of records which would confirm then as the worst ever side in the Premier League - and one of the poorest top-flight teams ever.
• Derby manager Paul Jewell: "It is difficult to accept a performance like this.
"We played well for the first 20 minutes but as soon as we concede a goal it is like a pack of cards and we just collapse.
"It is a horrible situation we are in and it is uncomfortable. As soon as we face a bit of adversity we have not got enough leaders or men to get us through it.
"Once they scored the difference in class was huge."
• Aston Villa boss Martin O'Neill: "We played very well today. Derby started very brightly and we were playing second fiddle.
"But we got the goal and the whole game changed. There was plenty of confidence about the side but we had to work hard and try to get the ball back.
"Petrov played very well last week and recreated that today.
"We have got everything to play for still this season, but we can't make any mistakes. We need to give ourselves a chance."
Derby: Carroll, Todd (Earnshaw 54), Moore (Leacock 54), Stubbs, Lewis, Mears, Ghaly, Savage, Jones (McEveley 59), Villa, Miller. Subs Not Used: Price, Feilhaber.
Aston Villa: Carson, Mellberg, Laursen, Knight, Bouma, Petrov, Reo-Coker, Barry (Salifou 80), Young (Berger 80), Carew (Harewood 73), Agbonlahor. Subs Not Used: Taylor, Routledge.
Goals: Young 25, Carew 26, Petrov 36, Barry 58, Agbonlahor 76, Harewood 85.
Ref: Keith Stroud (Hampshire).
BBC Sport Player Rater man of the match: Gareth Barry 7.68 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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