Frank Lampard came to Chelsea's rescue as defiant Everton threatened to spring an FA Cup fourth round shock.
Lampard slots home Chelsea's equaliser at Everton
Lampard slid a cool finish past Everton keeper Nigel Martyn with 17 minutes left to cap a period of sustained pressure from Jose Mourinho's side.
James McFadden headed home Nuno Valente's cross after 36 minutes to give Everton a deserved lead.
But Chelsea battled back and Martyn produced an outstanding display to earn Everton a replay at Stamford Bridge.
Everton suffered a blow before kick-off when leading scorer James Beattie was ruled out with a calf strain, forcing boss David Moyes to pair McFadden and Duncan Ferguson up front.
Maniche gave Everton their first anxious moment after 19 minutes when he shot only inches wide from 20 yards after he was left unmarked.
But Everton were more than a match for Chelsea and deservedly took the lead nine minutes before the interval.
Valente's cross was perfectly-flighted for McFadden, who rose to head past Chelsea keeper Carlo Cudicini.
William Gallas was then booked for a high challenge on McFadden, who required eight stitches in a cut below the knee at half-time.
And the Scot was in the wars again after 52 minutes when he collided with Cudicini as he chased a high ball.
He was led away with blood streaming from his nose, to be replaced by substitute Gary Naysmith.
Chelsea made a double change of their own on the hour, with Maniche and Asier del Horno replaced by Damien Duff and Carlton Cole.
It was a move that almost brought instant dividends as Cole nodded Duff's cross into the path of Hernan Crespo, who somehow blazed wildly over the top from six yards.
Crespo was then only inches away with a curling drive from just inside the area as Chelsea exerted total domination.
Everton were being tortured by Chelsea's possession football, and goalkeeper Nigel Martyn preserved their lead with a stunning save from Joe Cole's deflected shot.
But it was only a reprieve as Lampard deservedly equalised for Chelsea with 17 minutes left.
Gallas played in the England midfield man and he finally beat the defiant Martyn with a trademark finish.
Lampard then pulled a shot wide when well-placed before the outstanding Martyn pulled off another fine save from Arjen Robben.
Everton manager David Moyes:
"I thought it was a top performance, especially given that we were without a lot of players.
"They all deserve a massive pat on the back. We played the best side in the country and for the most part gave them a really good game.
"I thought it was going to be our day but Chelsea battled back as they always do. Their record of winning games and getting back into games in the second half is second to none.
"We tried to plug all the gaps and hold it together but Chelsea got the goal they needed."
Chelsea manager Jose Mourinho:
"He is a very important player and this is why he is getting big awards in Europe.
"The way we play helps him get into the box and he arrived at the right moment to score the equaliser for us.
"Goodison Park is a very difficult place to come at any time and this is a good result for us.
"We have survived and taken the game home. That is not to say we are already in the next round because the replay will be difficult, but it is a positive."
Everton: Martyn, Hibbert, Weir, Neville, Nuno Valente, Osman, Arteta, Davies (Anichebe 89), Kilbane, Ferguson, McFadden (Naysmith 54).
Subs Not Used: Wright, Hughes, Boyle.
Goals: McFadden 36.
Chelsea: Cudicini, Johnson, Gallas, Terry, Del Horno (Carlton Cole 59), Robben, Makelele, Lampard, Maniche (Duff 59), Crespo, Joe Cole (Huth 74).
Subs Not Used: Cech, Diarra.
Booked: Gallas, Huth.
Goals: Lampard 73.
Ref: G Poll (Hertfordshire).