The Blues struck twice in quick succession just before the interval, with a clinical Oscar strike and a Frank Lampard penalty giving the impressive home side a lead that proved unassailable after the break.
The result sees Rafa Benitez’s men climb three points above fifth-placed rival Tottenham in the hunt for Champions League football, while Swansea sits securely at ninth in the table having already insured its European participation – albeit in the Europa League – next term.
Chelsea made a number of changes from the side that beat Basel midweek, with Gary Cahill returning from injury to partner John Terry at the back and Juan Mata, Oscar and Demba Ba all recalled at the expense of Lampard, Victor Moses and Branislav Ivanovic
Swans boss Michael Laudrup handed starts to Wayne Routledge and Ki Sung-Yeung, as Luke Moore and Nathan Dyer made way.
After a slow start to the game, punctuated only by Ba's well-struck effort from range, it was the introduction of Lampard - who replaced the injured Ramires just before the half-hour mark - that sparked the encounter into life.
Chelsea's second all-time top goal scorer drove through the middle of the pitch to force Michel Vorm into a smart stop with a speculative effort from 30 yards, as Cahill sent a free header from the resulting corner inches wide.
That passage was to prove the catalyst to Benitez's side plundering a quick-fire double before the interval, as Lampard again drove through the heart of the Swansea team to feed in Oscar down the right channel, where he angled beyond Vorm to put the home side a goal up.
Moments later and on the stroke of halftime, Lampard doubled the lead and brought himself to within a goal of Chelsea legend Bobby Tambling's goalscoring record, giving Vorm no chance with a low, driven penalty after Leon Britton clumsily tripped Mata as he advanced into the box.
The second half continued in the much the same expansive manner as the first, with Ba going close with number of half chances, all of which Vorm proved equal too, as Michu and Angel Rangel threatened sporadically at the other end.
Mata's inventive cut-back narrowly evaded Ba at the far post as Chelsea sought to extend the lead, before Lampard's poor touch allowed Vorm to rush out and collect at the midfielder's feet.
The introduction of Neil Taylor - returning from a broken ankle picked up earlier in the season - provided the visiting side with a solitary positive to take away from west London, as Benitez's side saw out the remainder of the game in reasonable luxury.
Three points sees Chelsea enter the latter stages of the domestic campaign with its Champions League qualification ambitions in its own hands, though the club faces crucial games against Manchester United and Tottenham after the Europa League second leg semifinal against Basle on Thursday.
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