Midfielder Pedro comeback in the second half of the season continued as he let blaze a rocket from 25 yards to split the teams on 66 minutes.
The Spain international was afforded time and space to change direction in front of goal and drop his left-footed effort into the top corner.
Chelsea skipper Gary Cahill made it two in two matches for the England centre back when scrambling home 11 minutes from time.
And star playmaker Willian secured the win with a tap-in after striker Diego Costa had fed substitute Cesc Fabregas into the box.
The Ronald Koeman side [Everton] had chances to score, with Dominic Calvert-Lewin hitting the post and inform striker Romelu Lukaku squandering a number of half openings.
Costa and Eden Hazard both went close for the tourists.
But it was former Barcelona playmaker [Pedro] who finally found the net with is 12th goal of the season, before Gary Cahill capitalised on a goalkeeper Joel Robles mistake for his ninth strike of the campaign and the Brazilian [Willian] added a third.