The 21-year-old netted a trio of left-foot finishes in a barnstorming performance. Joey Barton had opened the scoring with a screamer and Kevin Nolan added two goals of his own.
Villa were awful, and John Carew's early penalty miss set the tone for a shambolic performance from Kevin MacDonald's side.
The rout spells the end of Barton's bizarre moustache, which the midfielder had refused to shave off until Newcastle won a Premier League game.
Newcastle received a harsh reintroduction to the top flight on Monday when they lost 3-0 to Manchester United at Old Trafford.
Chris Hughton picked an unchanged side and it looked like more of the same for the promoted side on nine minutes, when Ashley Young beat the offside trap, latched on to a Stiliyan Petrov through ball and drew contact from goalkeeper Steve Harper. A clear penalty.
But Harper was not called upon to stop Carew's spot-kick, as the Norwegian blasted it hopelessly over the bar.
Within three minutes of Carew's miss, Newcastle made him pay. Barton collected the ball three yards outside the Villa box and lashed a powerful drive into the top-right corner, although goalkeeper Brad Friedel may feel he could have done better.
It was the 27-year-old's first Premier League goal since October 2008, when he rifled in a penalty against West Bromwich Albion.
Barton might just be starting to come good on his boast he is the match of any midfielder in the country, but showed an unwanted side of his game with a late tackle on Petrov that earned him a yellow card.
Newcastle defended with a high line and continued to show frailty, as first Carew and then Young was played through. The former lacked the pace to get away, while the later used his arm to control the ball.
Then, just after the half-hour mark, it was two. Carroll rose high at the back post to head down a left-sided cross and Nolan sent a diving header goalwards. Friedel parried it, but Nolan pounced to net the rebound with a second header.
Villa were all at sea, and on 34 minutes they were breached again. Mike Williamson headed across the six yard box from a corner, Richard Dunne missed his kick and Carroll slammed a low left-foot shot into the right corner.
When England trailed Germany by three goals at the World Cup, Fabio Capello's introduction of Heskey from the bench caused outrage.
MacDonald did the same here, and there was a mixture of derision and jeers for the former international, who initially played on the right wing after replacing Marc Albrighton.
There was worse to come from MacDonald, as he brought defensive midfielder Nigel Reo-Coker on for Carew.
These inexplicable changes, coupled with the appalling result, might have hastened the end of MacDonald's reign as caretaker manager, though he will no doubt wonder what might have been had Carew converted his penalty.
Nonetheless, USA manager Bob Bradley's declaration of interest in the Villa Park vacancy seems ominous for MacDonald.
Newcastle came again, as Carroll latched on to a dropping ball in the Villa area and lashed another left-foot shot past Friedel.
Toon's most famous number nine, Alan Shearer, looked on approvingly from the stands as the present incarnation doubled his tally. How long until the clamour begins for an England call-up for Carroll?
He could have completed his hat-trick on 74 minutes, but saw his close-range shot repelled by the beleaguered Friedel.
Nolan added to the pain, hooking in from close range after Villa failed to clear a corner.
And in the dying moments of stoppage time, Carroll latched on to a Xisco through ball and found the bottom-left corner.
It was the fourth 6-0 scoreline in the first 18 Premier League games of the season, and certainly the most surprising. Newcastle are back.