Jose Mourinho's side scored four goals before half-time, and though they were unable to repeat the trick after the break, Andre Schurrle added a late fifth
Swansea were the architects of their own downfall at times, though, with Oscar profiting from a poor pass to open the scoring from 20 yards within the opening minute, and Diego Costa opening his account with a composed finish.
The striker added his second following a mistake from Federico Fernandez in the 34th minute, before he turned provider as Oscar made it four two minutes later.
Chelsea coasted to victory in the second half, with Andre Schurrle rounding off the scoring from close range late on.
Victory sees Chelsea move five points clear at the top of the table - second-placed Manchester City face Arsenal on Sunday – while Swansea remain in ninth after their heaviest defeat of the season.
With Leon Britton sidelined by a groin injury, Swansea were forced to play Gylfi Sigurdsson in a deeper midfield role, and it cost them almost instantly.
The Iceland international played a loose pass inside his own half that ricocheted off Tom Carroll to Oscar - the Brazilian punishing the mistake with a low drive from the edge of the penalty area.
Sigurdsson immediately went close to atoning for his error with a long-range effort that clipped the post on its way wide, but Swansea should have been further behind when Willian blazed over after 12 minutes.
Mourinho's side were in total control and, after Eden Hazard saw a low shot saved, they doubled their lead as Costa applied the finishing touch to a flowing move.
Oscar, Willian and Cesc Fabregas exchanged passes on the edge of the penalty area before the latter played in his Spain team-mate, and he emphatically fired beyond goalkeeper Lukasz Fabianski.
Another two goals arrived before the break as Chelsea punished some more slack Swansea defending, the first coming when Costa pounced on Fernandez's weak back pass and the second – Chelsea's fourth – going in two minutes later.
Willian powered through the Swansea midfield before finding Costa on the right, his cut back found Oscar and he fired high into Fabianski's goal.
There was still time for Willian to hit the crossbar before the break, but it mattered little to Chelsea, who threatened again early in the second half with Fabregas wasting a close-range effort.
After such a disastrous first half, things began to improve for Swansea as their pass-and-move football returned, but Chelsea's defence comfortably kept them at bay.
Patient play was the name of the game for the visitors and, after another period of possession, the ball fell to Hazard after 71 minutes - the Belgian unleashing a powerful shot that Fabianski was able to push away.
Substitute Schurrle added gloss to Chelsea's win with the fifth goal after 79 minutes, the Germany international ghosting into the penalty area to convert Branislav Ivanovic's low cross and seal an emphatic win.