Despite early pressure from the visitors, Swansea were ahead in the 20th minute thanks largely to a goalkeeping mistake from Jussi Jaaskelainen.
Angel Rangel broke free on the right-hand side of the box and his shot managed to squirm underneath the Hammers goalkeeper before rolling into the net to give Michael Laudrup's side the lead.
The visitors were rocked by the goal and failed to recover before falling further behind nine minutes later.
James Collins sold a back pass short to Jaaskelainen and Michu took advantage by easily slotting the ball into the bottom corner for his third goal of the season.
Swansea remained in control after the interval and could have been further ahead when Danny Graham was released by Nathan Dyer, but the striker's curling effort sailed agonisingly past the post.
However, Graham had his goal just moments later when Wayne Routledge delivered a cross for his teammate to easily finish from close range.
West Ham rarely threatened in the final stages and Dyer could have recorded a goal of his own but he fired his shot over the crossbar to keep the score at 3-0.