Chelsea win battle of Blues
Rooney even missed a late penalty as Everton were outplayed by the Blues, who also found the net through Emmanuel Petit and Mario Stanic, while Gary Naysmith's late strike provided scant consolation for the visitors.
Hasselbaink and Petit punished Everton with first-half goals.
Gianfranco Zola provided the assist on both occasions, playing Hasselbaink through on 26 minutes before setting up Petit just before half time.
Everton with Rooney out on the left flank were posing problems early on and Mark Pembridge wasted a clear opening as he volleyed Radzinski's knockdown just off-target.
Both teams were making too many unforced errors but Chelsea turned the game on its head with a superb move from inside their own penalty area on 26 minutes.
Lampard showed composure on the ball to turn inside before picking out Zola, who saw the forward surge of Hasselbaink and played a pinpoint pass into his strike partner's path.
The Dutchman was left to bear down on the Everton goal and made no mistake as he clipped his shot past Wright.
Having switched flanks as Everton settled back into a 4-4-2 formation, Rooney's first real impression on the game came after 31 minutes when he delivered a high cross which Campbell headed at Chelsea goalkeeper Carlo Cudicini.
That was quickly followed by a magnificent crossfield ball to
Pembridge, whom Everton boss David Moyes decided to withdraw shortly
afterwards as he replaced him with Gary Naysmith on 36 minutes.
The mistakes otherwise continued, however, with Lampard and Joseph Yobo probably the most dominant forces on each side.
Although Chelsea had the majority of possession, Zola was giving the ball away far more than normal, but his genius still managed to surface as he played a vital role in his side's second goal just before the break.
The Italian chipped a perfect lobbed pass to Petit, who just managed to beat the offside trap before swivelling onto the ball and sending his volley past Wright.
With Enrique de Lucas replacing Gronkjaer, it was not long before Chelsea were out of sight when Stanic rose above Li Tie to head home his side's first corner of the game on 68 minutes.
Everton brought on Scot Gemmill for Tie but Chelsea simply increased their lead three minutes later, with Hasselbaink cutting inside to beat Wright from 20 yards out to make it 4-0.
Everton were awarded a penalty with 12 minutes left when William Gallas was penalised for handball, but Rooney's misery was completed when Cudicini saved his spot-kick.
Everton did manage to pull a goal back from the ensuing corner, as Naysmith prodded home the ball from close range, but Chelsea were comfortably through to the fifth round of the competition.
CHELSEA: Cudicini, Melchiot, Babayaro, Gallas, Terry, Lampard, Stanic, Petit, Gronkjaer, Zola, Hasselbaink.
EVERTON: Wright, Pistone, Unsworth, Weir, Yobo, Pembridge, Tie Li, Gravesen, Campbell, Radzinski, Rooney.





