FA Cup - Everton topple Chelsea on penalties
Leighton Baines had his penalty saved just moments after scoring a spectacular 119th-minute free-kick to keep Everton in the competition.
Baines's brilliant goal cancelled out Frank Lampard's 104th-minute strike, and set up the dramatic denouement that ensured Chelsea will not win the famous trophy for the third season in a row.
The result increases the pressure on Blues boss Carlo Ancelotti, who must now lift his troops ahead of Tuesday's Champions League last 16 trip to face FC Copenhagen.
The Ivorian's outing looked like it might end early when he hurt a knee in a challenge - but after at least 10 minutes of grimacing and limping, he eventually shrugged off the knock.
However, he was a peripheral figure - unusually, given the obvious requirement to prove himself a better leading striker than Torres. His contributions were limited to a couple of long shots that whistled off target, and he stood in a strangely withdrawn role on the fringes of play.
Chelsea found themselves hassled and harried, but played on the counter-attack and carved out some decent chances.
Phil Jagielka glanced a header against his own post, while Tim Howard made two good saves from Florent Malouda - the second after the Chelsea man had snuck back onto the pitch after two minutes struggling to remove his wedding ring.
Chelsea thought they should have had a penalty in first-half stoppage time when Ramires knocked the ball past Howard and went to ground.
As Stamford Bridge roared for a spot-kick, referee Phil Dowd's assistant flagged in the opposite direction and Ramires was booked for diving.
Had the Brazilian kept running normally, he might have been fouled by Howard, but he began his fall before reaching the goalkeeper and the officials deserve credit for getting a marginal decision right.
The second half saw Chelsea assume a more dominant role, but Lampard and Drogba were denied by a succession of blocks from the heroic Jagielka and Sylvain Distin.
Fellaini thought he had won it for Everton in the 89th minute when he tucked away a rebound, but the officials got another key decision right, adjudging the big Belgian offside.
After 284 scoreless minutes in all competitions, Chelsea finally hit the net in extra time. Substitute Anelka cut the ball back from the right, Everton failed to deal with the danger and Lampard buried the loose ball.
It looked like it would be decisive until a late foul on Jagielka 25 yards out. Baines stepped up and curled a picture-perfect free-kick into the top-right corner with Cech rooted to the spot.
Baines looked to have blotted his copybook with the first miss in the shoot-out, but Anelka's shot - off a casual two-pace run-up - was superbly saved by Howard, and Cole fired over to allow Neville to settle an epic tie. Everton will meet Reading at Goodison Park in the fifth round.