The star duo both found the back of the net alongside Victor Moses as Antonio Conte's men made it back-to-back wins in the Premier League at Stamford Bridge on Saturday
Premier League top scorer Diego Costa continued his fine start to the season as Chelsea comfortably defeated champions Leicester City 3-0 at Stamford Bridge.
The Chelsea striker was on target within seven minutes with his seventh strike of the league campaign.
David Luiz hit the woodwork with a free-kick before Eden Hazard extended the hosts' advantage in a dominant first-half performance.
A Leicester comeback never looked likely and they failed to register a shot on target in a dreadful display, although only the post prevented a Luiz own goal after the break.
Victor Moses then sealed Chelsea's victory late on after a great flick from substitute Nathaniel Chalobah, giving Antonio Conte a welcome result in a week that has seen him fend off speculation over his future.
Conte's side have now won two consecutive league games, while Leicester – who left out Riyad Mahrez, Danny Simpson and Islam Slimani, perhaps with Tuesday's Champions League game against FC Copenhagen in mind – have lost all four of their top-flight away matches.
That leaves them eight points adrift of Chelsea and 10 behind leaders Manchester City, who have a game in hand against Everton later on Saturday.
Chelsea swiftly moved in front, Costa lashing home a left-footed strike which Kasper Schmeichel failed to get enough behind after the Spain striker had been left unmarked by Wes Morgan when Nemanja Matic flicked on a Hazard corner.
Luiz came close to doubling the hosts' lead midway through the half - striking the post with a dipping free-kick from 20 yards – but the second goal did arrive on 33 minutes.
Matic's throughball was not dealt with by three Leicester defenders and Pedro then found Hazard, who – after a fortunate ricochet – was able to race clear, round Schmeichel and coolly finish for his third league goal of the campaign.
Another Luiz free-kick was beaten away by Schmeichel at the end of a first half which saw Leicester offer very little.
Both sides had penalty claims turned down after the break – Christian Fuchs ruled not to have deliberately handled in blocking Pedro's shot and Victor Moses' challenge on Jeffrey Schlupp going unpunished by referee Andre Marriner at the other end.
Moses was then impressively denied by Schmeichel after being set up by N'Golo Kante - facing his former paymasters for the first time since leaving to join Chelsea in the summer - on a swift counter-attack as the hosts looked to put the result beyond doubt.
That intervention could have sparked a Leicester comeback, but Luiz was fortunate to see his attempted clearance from Marc Albrighton's threatening cross bounce to safety off the woodwork.
Claudio Ranieri brought on Mahrez and Slimani for the final 23 minutes, but Leicester were still unable to trouble Thibaut Courtois.
Morgan made an excellent sliding block to deny Kante, but a third goal did arrive on 80 minutes as Moses slotted home after a slick exchange with Chalobah, with Conte's men cruising to victory.