But with this display they will give Everton a good test in the next round such was the fluidity of their attacking.
Boro led 1-0 at half-time through David Wheater's 44th-minute goal but Marouane Fellaini and Louis Saha scored to give Everton a showdown against Manchester United.
Goals from Tim Cahill and Mikel Arteta gave Everton a deserved victory in front of Liverpool's new owners John W Henry and Tom Werner of New England Sports Ventures, who had issued a vote of confidence in Hodgson following their takeover.
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Howard has won the confidence of national manager Bob Bradley after establishing himself as a regular with English Premier League club Everton following a spell at Manchester United, where he was a fringe figure.
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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.
But a place in the Uefa Cup is still to be decided, with Everton needing a point at home to Newcastle to seal fifth place and European football.
Leijer had an unsuccessful trial with Everton as a youngster, but has rebuilt his career in the A-League.
The American's profligacy was soon forgotten as Everton crafted a superb opening goal.
Everton endured a dismal afternoon and are now only two points away from the relegation zone after the defeat.
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Yet Liverpool sits in seventh, three points behind its crosstown rival Everton and a colossal 12 points behind Sunday's opponent.
Andy Everton, a trumpeter with the orchestra, came up with the idea of a concert that was designed to raise awareness of deafness.
"People are always going to be linked with your players, especially if they see Everton as a club with not that much finance, " he said.
Against the run of play early in the second half, Everton added a third when Pienaar collected Neville's pass, turned, then curled a magnificent effort from 20 yards.
With Johnny Heitinga cup-tied and Sylvain Distin suspended, Everton had a new central defensive partnership in Yobo and Philippe Senderos - and the latter was very harshly penalised for a foul on Yannick Djalo.
Arsenal went into the match on the back of their stunning 6-1 Premier League win at Everton, a match in which Gallas was also on target, and the French defender made it two goals in two games with a huge slice of luck.
And in April, prior to United's FA Cup semi-final defeat against Everton, Ferguson blasted Benitez for labelling Everton as a "small club" and criticised the Spaniard for showing contempt to Blackburn when the Liverpool boss appeared to dismiss Sam Allardyce's side once Liverpool scored their second goal in a 4-0 win.
By 1931 Hornby was the owner of a multinational business, MP for Everton, and a millionaire.
The visitors had a gilt-edged chance to punish the miss when a slip by Birmingham centre-back Johnson allowed Everton forward Yakubu a strike at goal from 10 yards.
"I can make people happy at the weekend or on a Tuesday night when I'm playing for Everton by getting a result but when you can see a young person develop over six to eight months, they change, " he said.
The hosts went ahead with a thumping drive from Dmitri Likhtarovich but Marouane Fellaini drew Everton level from a Leighton Baines free-kick and Tim Cahill won it with 13 minutes remaining.
Following a free-kick where Gary Cahill made a nuisance of himself, Lee Chung-yong beat the Everton defence to a header and Sturridge was free to smash in from the angle.
Former Rangers and Scotland goalkeeper Andy Goram echoed Brown's sentiments and said he believed Smith, who had a spell in charge at Everton, could be a success in the English Premier League, but would be unlikely to take up another senior club role at home.
Niemi then raced from goal to make a vital block from Johnson as Everton attempted to regain a foothold in the game.
The summer deadline passed without the former Everton player getting a move from the Banks's Stadium.
Everton did find a way through before half-time, however, but even then it needed a helping hand.
Everton cruised to a 4-0 win over Fulham at Goodison Park to consolidate seventh place in the table.
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And Everton also had a big penalty shout when Baines went over Alex's outstretched leg, but referee Mark Halsey was unmoved.
Portsmouth were applauded off the pitch at Fratton Park having out-played Everton with only a combination of missed chances and brilliant goalkeeping denying them a point.
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