Jose Mourinho???s men recorded a 5-0 win to extend their Premier League leader to five points, with second-placed Manchester City facing Arsenal on Sunday at 3.30pm at Sports 1 HD.
It took 50 seconds for Chelsea to assert their authority, as Oscar picked up Gylfi Sigurdsson???s sloppy pass before driving goalwards and shooting into the bottom corner from 25 yards.
Within moments the hosts could have been level when Sigurdsson almost made up for his previous error in spectacular fashion, but his 30-yard strike clattered against the angle of bar and post.
That was Swansea???s best moment of the afternoon as Chelsea turned up the volume ??? Oscar shot at Lukasz Fabianski and Willian wasted the rebound in the 13th minute but their profligacy wouldn???t last.
After 20 minutes, a marauding passing move through the centre ended with Cesc Fabregas notching his 15th Premier League assist this season when Costa hammered home the second.
Just minutes prior, Oscar and Eden Hazard had narrowly missed as Swansea continuously failed to deal with Chelsea???s quick-fire passing and movement.
The Blues appeared to step up into different gears at the sight of their vulnerable opponents and Willian thundered a shot against the post with Swansea???s defence again bypassed.
Swansea???s unrelenting philosophy of passing from the back haunted them again for Chelsea???s third ??? Federico Fernandez???s lazy back-pass gifted Costa a one-on-one opportunity and he netted his 17th of the league season.
It took a further 76 seconds for Chelsea to rob the ball back and Oscar to deliver a curling shot from the edge of the box past Fabianski for the fourth goal.
Costa still found time to miss a gilt-edged chance for a first-half hat-trick when he dribbles around the goalkeeper but found himself too wide to score. He teed up Willian who hit the bar.
Perhaps with an eye on Tuesday???s Capital One Cup semi-final against Liverpool, Chelsea softened their frenetic approach in the second period while maintaining a steely control of proceedings.
Costa was denied a hat-trick as Mourinho withdrew him after 70 minutes but it was a substitute that added the fifth. After Eden Hazard and Branislav Ivanovic???s work on the right, Andre Schurrle scored from point-blank range two minutes after his introduction.