What looked a tricky fixture on paper against Ronald Koeman's team turned into a stroll for Antonio Conte's side who have recovered well from a shock opening-day defeat by Burnley.
Morata's clever header set up Fabregas to give Chelsea the lead in the 27th minute, the former Arsenal player sliding the ball past keeper Jordan Pickford with a deft finish.
Everton offered very little and Chelsea doubled their advantage five minutes before the break when Morata climbed to head home Cesar Azpilicueta's inviting cross for his second goal for his new club since signing from Real Madrid.
It proved a frustrating afternoon for Everton's Wayne Rooney who wasted one chance and was shown a yellow card while Gylfi Sigurdsson, making his first Premier League start for Everton, was given little chance to shine.
Chelsea keeper Thibaut Courtois was a virtual spectator and the hosts should have won by a clearer margin with Victor Moses and Pedro both guilty of squandering decent chances.
"We must be pleased with the performance. We played a really good game. We dominated and had plenty of chances," Conte said.
"The only negative thing is we should be more clinical. But there were a lot of positive things."
Chelsea moved into fifth spot with six points while Everton, who have now gone 23 matches without a win at Stamford Bridge, have four.
(Reporting by Martyn Herman; Editing by Clare Fallon)
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