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.
Morata then added his second goal of the season as he headed home Cesar Azpilicueta's cross six minutes before the interval, with Wayne Rooney and the Toffees unable to break down Conte's defence in the second half.
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Team news
Chelsea XI: Courtois, Azpilicueta, Luiz, Rudiger, Moses, Fabregas, Kante, Alonso, Pedro, Willian, Morata
Subs: Caballero, Bakayoko, Kenedy, Musonda, Batshuayi, Christensen, Tomori
Everton XI: Pickford, Keane, Williams, Jagielka, Holgate, Davies, Gueye, Baines, Rooney, Sigurdsson, Sandro
Subs: Lennon, Martina, Besic, Stekelenburg, Calvert-Lewin, Lookman, Kenny
Referee: Jonathan Moss (County Durham)
