Making his first start since November, Carroll proved to be an effective battering ram for the Hammers and their long-ball tactics. Sam Allardyce's men regularly launched the ball up to the England striker and while it was not easy on the eye, the tactic worked.
The former Newcastle man wore down the Swansea defence and stole away from his marker towards the end of the second half to head home Mark Noble's corner for just his second goal in claret and blue.
West Ham's plan to hit Carroll became apparent from the off. Winston Reid lumped the ball up to the big striker in the fourth minute, he knocked it down to Kevin Nolan but he shot wide.
Swansea had the majority of possession but West Ham were the most dangerous team. Carroll found space after dropping deep and laid the ball off to Mohamed Diame, who drew a good save from Gerhard Tremmel. Tremmel was called into action soon after, saving Nolan's shot with his feet.
Pablo Hernandez embarrassed Matt Taylor with a series of twists and turns before sneaking into the box, but the former Bolton man tracked back to block his shot. West Ham continued to punt the ball long. Swansea found it hard to deal with Carroll, who knocked a Ricardo Vaz Te pass into the path of Nolan, who drew a top save from Tremmel.
The visitors went in level at half-time but only thanks to Tremmel, who once again pulled off a top-draw save to deny Vaz Te.
West Ham started the second half as they ended the first. A clever backheel from Matt Jarvis released Nolan, who pulled the ball back for Carroll but he blazed over. Allardyce looked to Joe Cole for inspiration, the former Liverpool man coming on for the ineffective Matt Jarvis.
It looked as if the Hammers were destined to fail. Swansea's defence held strong and the home side continued to waste their chances. Diame was the next to blunder, almost finding the second tier of the Bobby Moore stand with an awful shot from yet another Carroll knock down.
After missing so many chances, there was a huge sense of relief when Carroll finally broke the deadlock. The England striker lost Ashley Williams in the Swansea box and leapt high before powering Mark Noble's corner past Tremmel. Swansea looked for an immediate response but an equaliser never came.