Two goals from Kevin Nolan sank the Swans at Upton Park as West Ham claimed a vital win over Michael Laudrup's side, despite the hosts being reduced to ten men.
Nolan volleyed home after 26 minutes to edge Sam Allardyce's side ahead, and then the midfielder doubled the lead on the stroke of half-time as he nodded home following a neat knock down from Andy Carroll.
England international Carroll, however, was sent off early in the second half following a collision with Chico Flores.
But the Swans failed to make any use of their man advantage as the Hammers comfortably held on for victory.
This defeat left the Swans just two points off the relegation zone, with 24 points from as many games.
The Swans made three changes to the starting XI.
Michael Laudrup brought Dwight Tiendalli into defence as Angel Rangel - who had a slight calf problem - moved to the bench, while Jordi Amat started in midfield ahead of Leon Britton.
The final change from the starting XI that beat Fulham saw Nathan Dyer, who played a big part in that win, handed his first start since December 15.
On the bench, David Ngog was included for the first time since his move from Bolton earlier this week.
WEST HAM: Adrian, Guy Demel, James Collins, James Tomkins, George McCartney, Stewart Downing, Marc Noble, Matt Taylor (Winston Reid, 79), Kevin Nolan (capt, Antonio Nocerino, 87), Matt Jarvis (Carlton Cole, 66), Andy Carroll.
SUBS: Jussi Jaaskelainen, Ravel Morrison, Roger Johnson, Marco Borriello.
SWANS: Gerhard Tremmel, Dwight Tiendalli, Chico Flores, Ashley Williams (capt), Ben Davies, Jordi Amat (Alejandro Pozuelo, 63), Jonathan de Guzman, Jonjo Shelvey (Pablo Hernandez, 70), Nathan Dyer (David Ngog, 76), Wayne Routledge, Wilfried Bony.
SUBS: David Cornell, Angel Rangel, Leon Britton, Roland Lamah.
After a even start to the game, the hosts made the early attempts on goal with James Tomkins firing over from 25 yards after Andy Carroll had nodded down a Stewart Downing cross.
Carroll was the focal point for the Hammers, with every cross aimed for the big striker.
And he played a central role in the hosts' opening goal after 27 minutes.
Matt Taylor found Carroll with a deep cross into the box, and when the England striker headed down for Kevin Nolan, the Hammers skipper controlled before volleying past Gerhard Tremmel from 18 yards.
The Swans looked for an instant reply, and they went close to getting one soon after.
Jonjo Shelvey sent a superb through ball for Wilfried Bony, but as the striker was about to shoot, James Tomkins' perfectly-timed sliding tackle denied the Swans forward.
The visitors kept plugging away, and when Shelvey raced towards goal while under pressure from James Collins, the midfielder went for goal by keeper Adrian was untroubled.
Ashley Williams then fired over after he latched onto a loose ball as West Ham failed to clear the danger from a Shelvey free-kick.
But the Hammers got the crucial second goal on the stroke of half-time.
After Carroll had won a corner by pressuring Williams, the striker then nodded the resulting delivery back to goal, and an unmarked Nolan glanced his header into the corner.
HALF-TIME: West Ham 2 Swans 0
The Hammers made a promising start to the second half, and it took a Ben Davies interception to deny Carroll after Jarvis had beaten Tremmel to the ball before crossing along goal.
At the other end, a de Guzman volley cannoned off Nolan before bouncing a yard wide of the far post and out for a corner as the Swans looked to cut the deficit.
Then Carroll, who had been a huge threat to the home side, was dismissed after referee Howard Webb showed him the red card after his arm connected with Chico following an aerial challenge.
The Swans needed to make the most of their opportunity, and Laudrup introduced Alejandro Pozuelo, Pablo Hernandez and David Ngog.
And Pozuelo was soon into the mix as he teed up Bony with a cross, but the striker's volley sailed high into the Hammers fans behind the goal.
The Hammers sat back as they looked to protect their lead, and they soaked up the pressure comfortably to bag three vital points.