Everton offered little in attack all afternoon and were deservedly beaten by a Chelsea side back on track thanks to successive top-flight wins in the past week, lifting them up to fifth place in the early league standings.
The first real opening of a one-sided first half fell the way of Pedro, who could not quite keep his overhead kick down when picked out by Morata.
The breakthrough moment arrived 27 minutes in through a perfectly executed finish from Fabregas, exchanging passes with Morata inside the box and casually slotting past Pickford on the volley.
Everton failed to register a single touch of the ball in their opponents' 18-yard box in the opening 45 minutes, and they were rightly two down before the half was out.
Morata added to his earlier assist with a second league goal in Blues colours, just about remaining onside to head past Pickford when spotted by Cesar Azpilicueta from deep after referee Jonathan Moss justifiably played advantage for an earlier challenge.
The slight change in system almost paid off instantly as Sandro Ramirez was slotted through by Wayne Rooney, only to see his shot - which appeared to be going wide - blocked by Antonio Rudiger inside the area.
Both sides struggled to find any real tempo to their game, with the next attack of any note culminating in Pedro shooting wide of the target an hour in.
Victor Moses should have done better when played through soon after, failing to get the beating of Pickford, while Pedro curled another one wide of goal.
Everton were unable to set up a grandstand finale as Ashley Williams's glanced header ended narrowly wide of the far post and Idrissa Gueye's shot was helped over the bar by Thibaut Courtois - his first and only save of a quiet afternoon.