Chelsea's advantage at the summit is now into double figures and Tottenham will take over as their closest challengers should they pull within 10 points by beating Stoke City on Sunday.
Antonio Conte's side
started with purpose, Pedro curling over from the edge of the area inside the first minute, but Chelsea struggled to break down Swansea following that early opening.
Indeed, it took an excellently worked move for Fabregas to open the scoring in the 19th minute.
Eden Hazard started the attack and linked up superbly with Costa before the ball was worked out to Pedro, who centred for Fabregas to stab into the bottom-left corner.
Only the fantastic reflexes of Fabianski denied Fabregas a second, the Swansea goalkeeper diving to his right to keep out the Spaniard's volley into the ground from a Victor Moses cross.
Chelsea continued to enjoy the better of the play but Conte saw his side pegged back on the stroke of half-time as Llorente provided a reminder of what they could have bought in January.
Sigurdsson lofted a free-kick from just inside the Chelsea half into the box and Llorente, who had been linked with the Blues last month, met the delivery with a thumping header that flew beyond the grasp of Thibaut Courtois.
Fabianski was required to preserve parity with a low stop down to his right to thwart the instrumental Hazard, and it was the Belgian who supplied the cross as Fabregas was cruelly denied by the woodwork.
Fabregas met Hazard's pull back with a thunderous drive that clattered off the crossbar with Fabianski beaten.
Swansea had a huge appeal for a penalty turned down despite Cesar Azpilicueta appearing to handle in the area, and there was more misfortune for the visitors as Chelsea regained the lead.
Pedro's low effort from outside the box appeared tame enough for Fabianski to handle, but the Pole somehow allowed it to creep under him and into the bottom-left corner.
Costa added gloss to the scoreline by volleying in Hazard's clever cross from close range to halt Swansea's resurgence under Paul Clement and take another step towards regaining the title, while also equalling a club record by securing their 12th successive home victory in all competitions
Chelsea's advantage at the summit is now into double figures and Tottenham will take over as their closest challengers should they pull within 10 points by beating Stoke City on Sunday.
Antonio Conte's side started with purpose, Pedro curling over from the edge of the area inside the first minute, but Chelsea struggled to break down Swansea following that early opening.
Indeed, it took an excellently worked move for Fabregas to open the scoring in the 19th minute.
Eden Hazard started the attack and linked up superbly with Costa before the ball was worked out to Pedro, who centred for Fabregas to stab into the bottom-left corner.
Only the fantastic reflexes of Fabianski denied Fabregas a second, the Swansea goalkeeper diving to his right to keep out the Spaniard's volley into the ground from a Victor Moses cross.
Chelsea continued to enjoy the better of the play but Conte saw his side pegged back on the stroke of half-time as Llorente provided a reminder of what they could have bought in January.
Sigurdsson lofted a free-kick from just inside the Chelsea half into the box and Llorente, who had been linked with the Blues last month, met the delivery with a thumping header that flew beyond the grasp of Thibaut Courtois.
Fabianski was required to preserve parity with a low stop down to his right to thwart the instrumental Hazard, and it was the Belgian who supplied the cross as Fabregas was cruelly denied by the woodwork.
Fabregas met Hazard's pull back with a thunderous drive that clattered off the crossbar with Fabianski beaten.
Swansea had a huge appeal for a penalty turned down despite Cesar Azpilicueta appearing to handle in the area, and there was more misfortune for the visitors as Chelsea regained the lead.
Pedro's low effort from outside the box appeared tame enough for Fabianski to handle, but the Pole somehow allowed it to creep under him and into the bottom-left corner.
Costa added gloss to the scoreline by volleying in Hazard's clever cross from close range to halt Swansea's resurgence under Paul Clement and take another step towards regaining the title, while also equalling a club record by securing their 12th successive home victory in all competitions.