After a quiet start, the game sprung into action just within half-an-hour. Carroll was able to nod the ball down for Kevin Nolan on the edge of the Swansea area, before the veteran player sent a left-footed shot into the bottom corner of Gerhard Tremmel's net.
The Hammers had another good chance in the 32nd minute, Matt Jarvis sending a dangerous cross in the direction of the Swansea box, but nobody could get on the end of it.
The East London outfit were eventually able to double their lead on the stroke of half time, as Nolan, again assisted by Carroll, lashed an effort into the bottom corner from six yards.
The Swans frantically tried to get themselves back into the game in the second half, Jonathan de Guzman and Jonjo Shelvey recording some chances on the hour, but West Ham's defence was able to thwart them.
Just a few minutes later, Carroll received a red card for a foul on Chico Flores. Referee Howard Webb judged the England striker to have swung an elbow towards the Spaniard.
The Welsh side, however, were subsequently unable to capitalise on their numerical advantage, and the match finished 2-0.
The Hammers, now out of the Premier League's bottom three, nonetheless face the prospect of losing Carroll for three games due to suspension.