The on-loan Liverpool striker was making his first start since November following injury and he marked the occasion with a fine display and a 77th minute header to settle an otherwise forgettable contest.
It was a very welcome win for West Ham, who collected three points for just the third time in two months, and eased a previously worrying slide towards the Premier League relegation zone.
Swansea, for all their pretty football, only sprung to life when Carroll's goal went in and Michu, who has now gone six league games without a goal, had an off-day playing on his own up front.
West Ham's plan to launch the ball to Carroll became apparent from the off. Winston Reid lumped it 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.
The Swansea goalkeeper was called into action soon after, saving Nolan's shot with his feet.
The visitors went in level at half-time but only thanks to Tremmel, who once again pulled off a top-draw save to deny Ricardo 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.
It looked as if the Hammers were destined to fail. Swansea's defence held strong and the home side continued to waste their chances.
Referee Lee Probert then failed to award the Hammers a penalty when Vaz Te's shot struck the arm of Chico Flores.
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 continued to push for an equaliser but it never came.