Morata impressed for the Blues with a goal and an assist on his Stamford Bridge debut despite a 3-2 opening-day defeat to Burnley, and the Spanish striker posted a similar return against Ronald Koeman's Toffees on Sunday.
Antonio Conte's title holders looked much-improved on their return to the Bridge after receiving a much-needed boost with a 2-1 win at Tottenham last weekend, and Fabregas - restored to the starting XI after serving a one-match ban - got the ball rolling by finishing Morata's header with a well-timed volley after 26 minutes.