The hosts were dealt a blow before the game when James Beattie was ruled out for three matches with a suspected calf strain.
With Alan Stubbs cup-tied and Matteo Ferrari injured, David Moyes had to reshuffle his pack dramatically with Duncan Ferguson and James McFadden returning and Phil Neville slotting into defence.
Three untried teenagers and unfit Gary Naysmith kept goalkeeper Richard Wright company on the bench.
Chelsea's Glen Johnson was taken ill before kick-off so Joe Cole deputised as Jose Mourinho made four changes to the team that drew with Charlton last week.
In truth both teams looked a little lethargic in the opening stages although Chelsea caused early problems for Everton particularly down the middle with Neville looking uncomfortable alongside David Weir.
Everton attempted to up the tempo in the 15th minute but Ferguson and McFadden didn't have enough quality or guile to cause John Terry and William Gallas any problems.
Simon Davies' shot, which cannoned of Asier del Horno, almost caught out Carlo Cudicini while at the other end Nuno Maniche skimmed Nigel Martyn's right-hand post with a 20-yard daisy-cutter.
Ferguson tried to get on the end of high ball after high ball lofted in by Tony Hibbert and, although the tactic wasn't pretty to watch, it was clearly rattling the Chelsea defence.
Chelsea finally began to take control of proceedings as Maniche, Claude Makelele and Frank Lampard tightened up their approach play.
A great move by Everton on 35 minutes should have brought the first goal as Kevin Kilbane turned beautifully to play in Ferguson who fed Nuno Valente, but no blue shirt could get on the end of his cross.
Just 30 seconds later Valente's pin-point cross saw McFadden rise above his markers to bury a header past a despairing Carlo Cudicini to give Everton a deserved lead.
Lassana Diarra was yellow carded after a late challenge on McFadden who needed stitches for a nasty leg wound.
Arjen Robben's excellent 25-yard free-kick almost beat Martyn with two minutes of the half to go.
It was Everton who started the second half brightly although Joe Cole headed Lampard's 49th minute cross straight at Martyn.
Damien Duff and Carlton Cole replaced Maniche and Del Horno on the hour as Mourinho sensed the game was getting away from his side.
Hernan Crespo missed a sitter on 62 minutes firing well over the bar as edginess began to creep into Everton's play.
Terry skied a close-range effort over the bar on 72 minutes before Martyn produced a fine save from Robben's deflected effort.
However, Chelsea were not to be denied and, after 74 minutes, Gallas played in Lampard to bury his shot into the bottom right-hand corner of Martyn's net.
Chelsea almost scored a second after the Everton keeper spilled a Crespo shot but reclaimed the ball just before Carlton Cole could pounce.
Chelsea should have won the game with ten minutes left but Crespo's weak effort was easily collected by Martyn.
The veteran former Leeds keeper was again the hero moments later when he pushed a Robben cross away.
Seventeen-year-old forward Victor Anichebe made his Everton debut when he replaced Davies as Moyes looked to relieve the Chelsea pressure.
The game ended all-square but Ferguson could have won the game for Everton in the dying seconds when his shot just shaved Cudicini's post.