The straightforward victory was inspired once again by Didier Drogba, who set-up the first, scored the second and terrorised Everton all afternoon.
Jose Mourinho made one change for Chelsea following the energy sapping 2-0 win at Bolton on Saturday - Arjen Robben for Joe Cole.
In the opening period the hosts' play looked sluggish, while Everton, for their part, were happy to sit back and defend deeply.
A brilliant left wing cross by Asier del Horno after 20 minutes failed to reach Drogba or Hernan Crespo, as the strike duo failed to anticipate the flight of the ball.
Michael Essien's piledriver sailed over the bar seconds later, but inevitably Chelsea kick-started their display with a goal.
The strike came from free-scoring Frank Lampard after 28 minutes, when he steered the ball through a crowd of bodies into the bottom corner of Richard Wright's goal from the edge of the area.
The goal was created by Drogba, who having backtracked 30 yards to dispossess Tim Cahill, fed a gloriously simple pass into the England man's path to set-up his 20th of the season.
James McFadden produced a fine tackle to dispossess Robben in the area shortly before the break and although Mourinho jumped to his feet demanding a penalty, the referee rightly adjudged the challenge to be legal.
Everton's best effort of the half saw a Cahill shot from 20 yards deflected away from goal by John Terry.
The hosts were forced to bring on Carlo Cudicini for Petr Cech at the break after the Czech Republic shot-stopper suffered a gash in his knee that required nine stitches following a collision with William Gallas.
Everton's day went from bad to worse when Lee Carsley was given a straight red card after 47 minutes for a reckless tackle on Drogba. It was a harsh decision.
Drogba got his reward for a fine performance by doubling the lead in the 62nd minute.
Lampard's corner dropped to the incoming striker who powered a great header past Wright from 10 yards.
Chelsea found a third 16 minutes from full-time after Everton put all their players on the goalline to prevent Lampard from scoring with an indirect free-kick eight yards out.
But when the ball was cleared it fell to Essien who raced back into the area before firing a right-foot rocket between Wright and his near post.