Chelsea booked an FA Cup fifth-round tie against Colchester after cruising past Everton in their replay.
Robben gave Everton a torrid time
Everton had Iain Turner, 22, in goal after Richard Wright, named as a starter, was injured in the warm-up.
Turner was first beaten when Arjen Robben converted following good work from Hernan Crespo, and then he saw Frank Lampard score from the spot.
Crespo made it 3-0 at the break and after Mikel Arteta made it 3-1 from the spot John Terry struck late on.
But it was the injury to Wright that will live long in Everton's memory - the first-choice keeper injuring himself before the game had even started.
Turner came in as a replacement, but soon realised after the first whistle that his FA Cup debut for Everton was unlikely to be covered in glory.
Chelsea peppered Turner's goal with swarms of attacks, led by the creative triumvirate of Robben, Crespo and Eidur Gudjohnsen.
However, it was centre-back Robert Huth who had the first effort on Everton's goal, with his header from a corner cleared off the line by Tony Hibbert.
Turner then had to be alert to save low from Gudjohnsen and Robben, but could do nothing about the opener which involved the same two players.
Gudjohnsen played a long ball to Crespo, who chested then flicked the ball into the path of Robben, who dinked the ball over Turner.
Lampard increased their lead soon after when he converted a penalty won by Shaun Wright-Phillips.
Just before the end of the half Crespo got his reward for a scintillating display when he eluded the Everton defence to head past Turner.
Arteta gave the away side and fans some winter cheer when he slotted home a penalty after Huth handballed James McFadden's shot.
But captain Terry restored Chelsea's advantage and put the icing on cake for the Premiership leaders with a vicious strike that flew past the unfortunate Everton keeper.
Chelsea assistant manager Steve Clarke:
"We were great against Everton and great against Liverpool on Sunday, but didn't get any credit.
"I don't know why we don't.
"The FA Cup is high on our list of priorities. We want to win the FA Cup, Premiership and Champions League."
Everton boss David Moyes:
"I thought the side did fine, but I was upset with the way we played in the first half.
"We over did it at times and Chelsea played the ball behind us.
"We tried to play small intricate passes, but got caught out time and time again. I didn't think a lot went for us."
Chelsea: Cudicini, Johnson, Huth, Terry, Gallas, Gudjohnsen, Wright-Phillips, Lampard (Geremi 79), Essien, Robben (Joe Cole 64), Crespo (Maniche 45).
Subs Not Used: Cech, Del Horno.
Goals: Robben 22, Lampard 36 pen, Crespo 39, Terry 74.
Everton: Turner, Hibbert, Weir, Ferrari, Neville, Nuno Valente (Davies 45), Arteta, Kilbane, Osman (Carsley 82), Cahill, Beattie (McFadden 45).
Subs Not Used: Wright, Naysmith.
Booked: Nuno Valente, Cahill, Carsley.
Goals: Arteta 72 pen.
Ref: P Dowd (Staffordshire).