Mason Mount replaced the injured Matteo Kovacic in just one change to the Blues' side that got the better of Liverpool in the Emirates FA Cup, whilst Carlo Ancelotti faced off against his former side.
Everton were picked apart inside the first 14 minutes when Pedro cut in from the left to find Mount, who fired beyond Jordan Pickford after swivelling inside the area.
A free-flowing move after four minutes saw Willian drill a low shot from the right at Pickford, who was equal to the task with a smart block after the defence went to sleep.
It was two inside three minutes after Ross Barkley's through ball sent Pedro clear and the Spaniard made no mistake with a composed finish.
Everton could've gone on the score-board after 25 minutes as possession turnover from Kurt Zouma ended with Dominic Calvert-Lewin who failed to beat Kepa Arrizabalaga in a one-on-one situation.
An injury to Bernard late in the first half ended his time on the field, as Theo Walcott replaced the Brazilian following the start of the second half.
The Blues secured a third six minutes after returning from the tunnel when Willian nestled the bottom-left corner from 20-yards after the defence backtracked.
It was four two minutes later when Willian played provider to Giroud, who stuck out a leg from four yards to tuck past a rooted Pickford.
Pedro was in for his second and the side's fifth minutes later with a clear shot on goal after a dummy, but Pickford smothered the danger.
The Blues still probed for more towards full-time while the Toffees attempted a comeback, but victory went to the hosts in the end.