Mikel Arteta's early free-kick and two second-half strikes from Tim Cahill put the Toffees in command.
He failed to make an impact on Merseyside and did not appear in the Toffees first team.
Louis Saha gave the Toffees the lead when he headed past Petr Cech from Leighton Baines' right-wing corner.
Jermaine Beckford and Phil Jagielka both missed their spot-kicks for the Toffees to give the Bees a famous win.
The Toffees fell behind when Stephen Hunt, Andy Dawson and Dean Marney scored for Hull in the first 28 minutes.
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Sylvain Distin's tap-in from a corner appeared to put the Toffees in control of the round of 32 first-leg tie.
The latter match at Goodison Park saw the Toffees hit back to draw 3-3 with two goals in injury time.
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The Toffees only just shaded the first half and Mikel Arteta's deftly struck shot was well saved by Mark Schwarzer.
The Toffees played well at Stamford Bridge and were unlucky to be 2-1 down on aggegate going into the second leg.
The Toffees, without their top scorer Tim Cahill, relied on Saha, Rodwell, Marouane Fellaini and Diniyar Bilyaletdinov to provide the bullets.
The Toffees appear to relish the role of underdogs but regularly stumble when there is an expectation placed on their shoulders.
The England defender insists the Toffees must improve their performance against the Gunners if they are to add to their points tally.
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The Toffees almost went ahead in the 13th minute, left-winger Jo Potter's 15-yard shot forcing goalkeeper Emma Byrne into an excellent diving save.
But Hunt had drifted in from the left and, with the Toffees defence sleeping, pounced to lash in the loose ball from eight yards.
Everton boss David Moyes welcomed back Tim Cahill after a two-month injury lay-off but the Toffees sorely missed the suspended Mikel Arteta's creativity in midfield.
Yet the Toffees were made to pay a high price when the statuesque Marouane Fellaini catastrophically slipped outside his own penalty area in the seventh minute.
Goals in either half from Gary Cahill and Daniel Sturridge left the Toffees three points off the drop zone and prompted a gloomy appraisal from Moyes.
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Blues should push both the Gunners and last season's runners-up Everton, though it's the Toffees who are likely to again provide the greatest threat to Arsenal's crown.
City upped the tempo midway through the second half and pinned the Toffees in their own half, with the away side retreating and comfortable in containing their hosts.
On-loan Brazilian striker Jo scored five times for the Toffees since arriving in January but has returned to Manchester City with Everton unable to afford a permanent switch.
Three strikes in three minutes downed the Toffees as Roberto Martinez's team move into the last four -- their best ever performance in the historic English cup competition.
The Toffees had been booed by their fans after a 1-0 defeat by Newcastle in the Premier League on Saturday and were looking to atone at Griffin Park.
"It looks like it is the same as Robin van Persie's injury, " added the Scot before his side's Europa League clash with Sporting Lisbon, which the Toffees won 2-1.
As in the first leg, when they were forced to weather a spell of sustained Olomouc pressure, the Toffees looked some way off the pace during the opening exchanges.
The Toffees, leading 4-0 from the first leg, had Tony Hibbert sent off for a foul on Jakub Petr and Lukas Bajer hit the bar from the resulting free-kick.
His spell out will be a huge blow to the Toffees as they continue to chase a European spot and hope to further their run in the FA Cup.
The victory - a sixth in succession at home - equals a club record in the Premier League and lifts the Toffees up to eighth, four points behind Aston Villa.
Paul Lambert's Villa had been 3-1 up against Everton at Goodison Park, before two goals from Marouane Fellaini -- the second in injury time -- rescued a point for the Toffees.
The Toffees felt they did enough to merit victory in the original tie at Goodison Park, which ended 1-1, and set out as if desperate to make up for that missed opportunity.
The Toffees boss also revealed it took a half-time dressing down to inspire Everton to a win against Middlesbrough and reach an FA Cup semi-final for the first time in 14 years.
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