Cesc Fabregas, restored to the team in place of Nemanja Matic, was making his 300th Premier League appearance and the former Arsenal star marked the milestone in the 19th minute with his 46th goal in the competition.
Picked out inside the penalty area by Pedro’s cut-back, Fabregas nimbly adjusted his stride before clipping his shot past Lukasz Fabianski.Despite being out-played for much of the first half, Swansea snatched an equaliser seconds before the interval at Stamford Bridge.
Gylfi Sigurdsson’s long free-kick caught the Blues napping and Spanish striker Fernando Llorente rose to head powerfully beyond Thibaut Courtois.
But Chelsea’s dominance was rewarded in the 72nd minute when Pedro Rodriguez’s routine long-range effort slipped past a weak attempted stop by Fabianski.
Diego Costa wrapped up the points when he finished off Eden Hazard’s pass in the 84th minute for his 17th goal of the season.
With second placed Manchester City’s scheduled derby against Manchester United postponed due to their rivals’ League Cup final date with Southampton on Sunday, Chelsea have opened up a huge lead at the top.
Third placed Tottenham can trim Chelsea’s advantage to 10 points if they beat Stoke on Sunday.