It was a first-half that was dominated by The Blues with half-chances for David Luiz and Pedro, however goals from Fàbregas and Morata in the 26th and 40th minutes secured the three points fairly early.
The second period had chances few and far between, with Sandro Ramírez, Pedro, Ashley Williams and Willian going close but the afternoon belonged to Antonio Conte's men.
Getting into the groove
After an sub-par opening performance in the 3-2 defeat to Burnley, Chelsea bounced back last week with a 2-1 win over Tottenham, and they looked to continue that against Ronald Koeman's side ahead of the international break.
Young goalkeeper Jordan Pickford had been impressive thus far since his big-money move from Sunderland and continued to show his talents, making good saves from Luiz and Pedro.
Proving critical at the right time
The Blues continued to turn the screw after those opportunities in the opening 15 minutes, and they were eventually rewarded for their constant pressure on Everton as they took the lead in the 26th minute.
It was slick play from the home side as they played a free-kick down the right into the feet of Willian, the ball made it to Fàbregas who played a one-two with Morata before poking it into the bottom corner past Pickford.
Morata turned from provider to scorer in the 40th minute as he doubled Chelsea's lead, it was poor from the Everton defence as César Azpilicueta's cross sucked Michael Keane under the ball and left Pickford in no man's land. Morata took advantage of the situation as he rose highest to head home.
Starting to become end-to-end
The Toffees came out for the second period looking a bit more positive and certainly looked a lot more threatening as they had some decent opportunities.
Their first real chance of the afternoon arrived in the 50th minute in a rare lapse in concentration from Conte's side, Wayne Rooney bombed forward before playing it through to Sandro but he sent it wide of the mark.
It got worse for Sandro as he nearly gave away what should have been a third for the home side, he was dispossessed which led to the ball landing at the feet of Pedro who opted to aim for the near post as opposed to hitting it across and it went wide.
Gylfi Sigurðsson looked to keep up his good form from Thursday's draw as he whipped an excellent ball into the mixer in the 84th minute, it found the head of Williams who had all the time in the world but somehow put it wide of Thibaut Courtois' post.