Carroll ignored personal turmoil to earn three vital points for the Magpies.
The powerful striker's place in the team was in doubt after a week which had seen him answer charges of assault and have his car torched while on bail.
But the England hopeful ensured that he ended the week on a high as he pounced to power a header past Robert Green after Nolan had cancelled out Carlton Cole's first goal of the season.
The result catapults the Magpies up to ninth in the table, while Avram Grant's team remain rooted to bottom spot.
The early signs had looked good for the home side. Captain Matthew Upson returned to the starting XI along with Valon Behrami, who had been out for a month with a knee injury.
Cole also showed some early encouraging glimpses as he made his first start for over a month.
The home side could have been ahead inside four minutes had Danny Simpson not cut out Frederic Piquionne's dangerous low cross which was intended for Victor Obinna at the back post.
Cole then played a clever one-two with Obinna inside the box but he dithered on the ball, allowing Fabricio Coloccini to clear.
West Ham dominated possession early on, pressuring the visitors down the flanks through Obinna and Piquionne.
And they had their reward in the 12th minute when Piquionne latched on to Mark Noble's brilliant through-ball before squaring from the left for Cole, who tapped in from five yards.
The Magpies appealed for offside but the linesman did not flag and replays suggested he made the right decision. The visitors hit back 10 minutes later when they levelled through Nolan.
Carroll, whose physical presence had troubled Upson early on, outjumped his two markers to nod Joey Barton's cross to Nolan who smashed the ball past Robert Green in front of the travelling fans.
Carroll was bailed to live with club captain Nolan on Monday after appearing in court charged with assaulting an ex-girlfriend, and the team-mates embraced after the strike.
Newcastle manager Chris Hughton remained on the sidelines for the majority of the first period as his side started to assert more control on the game, but it was West Ham who had the next big chance.
Obinna raced down the left before shaking off two markers to fire a dangerous low ball across the box but no-one could find a touch.
Newcastle goalkeeper Tim Krul did well to hold on to a high Noble cross with Piquionne lurking at the back post as West Ham looked to snatch the lead just before the break.
Newcastle laid siege to West Ham's goal with a flurry of late attacking play but the home side held on to go in 1-1 at the break.
Newcastle had the first chance of the second period when Nolan cushioned Barton's cross into the path of Carroll who paused before volleying at Green.
Herita Ilunga, who had been out for six weeks with a leg injury, then replaced Upson who was left shaken by an aerial challenge with Carroll.
The visitors were starting to dominate thanks to some impressive attacking ball retention and smart play down the left through Jonas Gutierrez.
The Argentina midfielder launched a clever ball over the top, but as Shola Ameobi raced through he was harshly adjudged to have fouled Hammers centre-back Danny Gabbidon.
Gutierrez then played in Carroll only to see Gabbidon snatch the ball with a sliding tackle inside the box.
Da Costa was taken aside for a word with referee Chris Foy after clattering into Ameobi but did not receive a booking.
Benni McCarthy then replaced Piquionne, who had picked up an injury.
The second Newcastle goal arrived when Barton whipped a cross from the right into the box to find the unmarked Carroll, and he powered a header past Green to put the Magpies ahead with little over 20 minutes left. It was his fifth goal of the season.
West Ham pushed for an equaliser but almost paid the price for over-committing when Barton broke and fired a deflected 25-yard shot which looped on to the roof of Green's net.
Grant looked to increase his attacking options by replacing Behrami with Mexico winger Pablo Barrera but Newcastle continued to dominate.
Jose Enrique rushed at the West Ham defence but Lars Jacobsen stepped in to deflect his shot over the bar.
Ameobi saw a deflected effort drift just wide with Green rooted to his line with 10 minutes left.
The Hammers fans started leaving in their droves as the match neared its end, and those who stayed booed the home team off after Foy blew the full-time whistle.