Antonio Conte's side suffered a shock 3-2 defeat to Burnley at home on the opening day of the season and their victory over Tottenham at Wembley last time out owed much to doggedness and some timely slices of luck.
But the Blues preyed mercilessly upon an Everton side who showed signs of the toll trips to Manchester City and Hajduk Split this week had taken.
Fabregas was one of the villains against Burnley as he was sent off, but orchestrated his opening goal before the half hour.
There were suspicions of offside when Morata doubled the lead five minutes before the interval, but the flag stayed down and Everton's hopes were seldom raised thereafter.
Conte's immediate concern will now be looking for an end to the Diego Costa saga before the transfer window closes next week, while Chelsea travel to Leicester City after the international break.
Pedro joined compatriot Fabregas in earning a recall to the Chelsea starting XI and the former Barcelona winger teed himself up to send a 10th-minute overhead kick beyond the crossbar.
Both sides' 3-4-3 setups largely cancelled each other out during the opening stages, but Everton were always more minded towards defence and paid for inviting Chelsea on to them in the 27th minute.
Fabregas saw the move through from beginning to end – finding Willian on the right flank before taking possession back and laying the ball in to Morata.
There was a touch of fortune as his international colleague erred and it ricocheted back into Fabregas' path, but the playmaker produced an excellent first-time finish with the outside of his right boot.
Chelsea proceeded to tighten their grip on Ronald Koeman's men, with Wayne Rooney and Idrissa Gueye forced into carelessly coughing up possession as a rumbling attacked ended with Morata slipping free of Michael Keane to head home Cesar Azpilicueta's pinpoint cross.
Rooney tasted defeat for the first time since his Everton return, but it was the former England captain who looked to rouse the visitors after the interval, driving at the Chelsea defence and threading a deftly weighted pass that fellow forward Sandro Ramirez greeted disappointingly with an ungainly swipe.
Conte's men were not about to let their control slip and Victor Moses shot into the side netting after being released by Willian's backheel.
Everton's club record signing Gylfi Sigurdsson would have had designs on hauling Koeman's side back into the contest, only to suffer the indignity of being nutmegged by Pedro before the tireless winger fired wide with an hour played.
Rooney's frustrations earned him a booking for dissent, while Michy Batshuayi intercepted a sloppy backpass from Phil Jagielka to prompt an attack that ended with fellow substitute Tiemoue Bakayoko having a shot blocked.
Ashley Williams almost had a rare goal when his spiralling attempt on the turn landed on the roof of the net and the Wales centre-back headed wastefully wide with five minutes remaining, but Everton would have no reward for their toil.
