Blues manager Thomas Tuchel opted for five changes from the win away to Liverpool, as Kai Havertz, Kurt Zouma, Matteo Kovacic, Marcos Alonso, Callum Hudson-Odoi were drafted into the line-up.
The hosts dominated possession in the early stages of the encounter, although they only had a first-time strike from Jorginho to show for their efforts in the opening 20 minutes.
That all changed on 30 minutes when Tuchel's side were gifted the opening goal after Toffees defender Ben Godfrey deflected Alonso's cross into his own net.
The Blues nearly bagged a second goal five minutes before the break when Hudson-Odoi slipped Alonso clear on goal, but Pickford got a strong hand to the Spaniard's strike.
The hosts carried that dominance into the second half, which eventually resulted in a penalty being awarded for Pickford's foul Havertz in the box.
Jorginho resumed penalty-taking duties and calmly sent the Everton shot-stopper the wrong way to double Chelsea's lead on 63 minutes.
While Everton failed to trouble Blues shot-stopper Edouard Mendy, Chelsea looked to add their tally in the latter stages but Pickford produced two saves in quick succession to deny Timo Werner and N'Golo Kante.
Nevertheless, the two goals were enough to seal three points for the Blues who sit fourth on the log, four points ahead of fifth-placed Everton.