The Blues struck twice in quick succession just before the interval, with a clinical Oscar strike and a Frank Lampard penalty earning the home side a lead that proved unassailable after the break.
The result sees Rafa Benitez's men move three points clear of fifth-placed rivals Tottenham in the hunt for Champions League football, while Swansea sit securely at ninth in the table having already ensured their European participation - albeit in the Europa League - next term.
Chelsea made a number of changes to the side that beat Basel in 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, Branislav Ivanovic and Fernando Torres.
Swans boss Michael Laudrup handed starts to Wayne Routledge and Ki Sung-Yueng, meanwhile, 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 goalscorer drove through the middle of the pitch to force Michel Vorm into a smart stop with a speculative effort from 30 yards before Cahill sent a free header from the resulting corner inches wide.
That passage was to prove the spark as Benitez's side plundered a quick-fire double before the interval. Lampard again drove through the heart of the Swansea team to feed Oscar in the right channel, who angled a shot beyond Vorm to put the home side a goal up.
Moments later and on the stroke of half-time, Lampard then doubled the lead and brought himself to within a goal of Chelsea legend Bobby Tambling's goalscoring record by giving Vorm no chance with a low, driven penalty after Leon Britton had 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 their 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 visitors with a solitary positive to take away from west London, as Benitez's side saw out the remainder of the game in reasonable luxury.
The three points see Chelsea enter the latter stages of the domestic campaign with their Champions League qualification ambitions in their own hands, though they face crucial games against Manchester United and Tottenham after the Europa League second leg semi-final against Basel on Thursday.