The 21-year-old England international's 10th goal of the season cemented a priceless victory for the Magpies after Scouser Barton's 80th-minute strike had restored their lead.
Skipper Kevin Nolan, another native Liverpudlian, had got the Magpies off to the perfect start with a 15th-minute opener, but Dirk Kuyt looked to have snatched a point for the visitors when his 50th-minute shot was deflected past keeper Tim Krul by the unfortunate Steven Taylor.
A delighted crowd of 50,137 had arrived determined to voice their fury at owner Mike Ashley's decision to sack Chris Hughton, and they did just that.
However, they left delighted with what they had seen as Pardew's charges responded in the only fashion they could.
As traumatic weeks go - and Newcastle have had a few in recent times - the last one on Tyneside has been right up there with the most trying, and there was a rebellious air around St James' once again in the run-up to kick-off.
The Toon Army made their feelings abundantly clear outside the stadium before the game, and did so in greater numbers once it was under way.
There were repeated choruses of "Stand up if you hate Ashley", "Get out of our club" and "There's only one Chris Hughton" among some less savoury offerings, while one banner read simply, "Thank you, Chris".
Indeed, as Pardew made his way to the dug-out for the first time, he did so almost unnoticed.
But both he and Ashley, sitting alongside managing director Derek Llambias, were on their feet within 15 minutes as the focus turned to what was happening on the pitch rather than off it.
The opening goal may have been fashioned on Merseyside, but it did not go to the men in red as two Scousers combined to open the door.
Barton's free-kick was floated perfectly to the far post for Carroll to win a muscular challenge with Sotirios Kyrgiakos and head down for Nolan to fire home his eighth of the season from close range.
The sense of unity fostered by Hughton during his tenure was there for all to see as Nolan was mobbed by his team-mates with the Toon Army celebrating.
Krul had earlier had to palm away a Kyrgiakos snapshot after referee Lee Mason, whose display was at times mystifying, awarded the visitors a soft free-kick for Jose Enrique's challenge on Glen Johnson.
But in an open encounter, both keepers had to remain alert throughout with Liverpool moving the ball well in an attempt to create space for the returning Fernando Torres, while Newcastle relied largely upon the physical presence of Carroll and strike partner Shola Ameobi.
The pair combined to great effect on the half hour when Carroll blasted in a low drive from Ameobi's lay-off which forced Jose Reina into a smart save, and the latter saw a 36th-minute effort fly just wide after it clipped Martin Skrtel's heels with the keeper already committed.
In the meantime, Enrique had been in the right place at the right time to keep out Raul Meireles' shot after it had been deflected towards goal by David Ngog, and Kyrgiakos headed a Meireles corner across the face of goal in first half injury time with Liverpool making a big push.
That trend continued after the restart and the visitors were level within five minutes, thanks in part to a slice of good fortune.
Kuyt did well to trick his way past Sol Campbell, but his shot was deflected past Krul by the unwitting Taylor and crept inside the far post.
Liverpool flexed their muscles and could have taken the lead twice within seconds as Torres first headed straight at Krul and then failed to beat him one-on-one after getting in behind a ragged home defence.
However, the Magpies responded and went close themselves when Barton crossed from the left for Carroll to dive in and head over as the ball dropped just over Skrtel's head.
Substitute Nile Ranger, on for the injured Ameobi, might have announced his arrival in style when he ran on to Carroll's 64th-minute knockdown and eased Skrtel off the ball, but his shot from a tight angle flew wide of the far post.
But they took the lead once again with 10 minutes remaining when Carroll and Ranger both helped on Krul's clearance and Barton stole in to snatch all three points.
The stage was set for a nervy conclusion, but Carroll prompted a collective sigh of relief when he crashed home a superb left-foot strike from 25 yards to wrap up a vital win.