United competed until the 59th minute when Mike Williamson fouled Luis Suarez for a penalty that Dirk Kuyt converted.
Dirk Kuyt's close-range finish three minutes before the interval looked to have secured Liverpool a slender lead.
Inter Milan midfielder Sneijder netted the winner when he headed Dirk Kuyt's near-post flick-on past a stranded Cesar.
The Black Cats fell behind to a Dirk Kuyt first-half penalty after John Mensah had fouled Jay Spearing.
Kingson also played his part when he made a good low save to deny Dirk Kuyt's placed effort.
Craig Bellamy added a second with a low finish and Dirk Kuyt scored a third after a quick break.
Dirk Kuyt said he hoped that this Dutch team could triumph where the teams of 1974 and 1978 fell down.
With seconds remaining, Liverpool won a corner on the right which Gerrard delivered on to the head of Dirk Kuyt.
In Gerrard's absence they played Dirk Kuyt in the position behind Fernando Torres and he was nullified by De Jong.
The Gunners trailed 1-0 at the break after an awful opening 45 minutes that had seen Dirk Kuyt score for Liverpool.
Sulley Muntari (calf) and Kieran Richardson (hamstring) both limped off before Dirk Kuyt opened the scoring with the hotly contested 34th-minute penalty.
El Zhar follows Steven Gerrard, Fernando Torres, Dirk Kuyt, Yossi Benayoun and Daniel Agger in committing his long-term future to the club.
However, Hodgson has been boosted by better news on strikers Fernando Torres and Dirk Kuyt, and defenders Martin Skrtel and Glen Johnson.
Raul Meireles pinged a corner to the back post which the tall forward nodded back into the six-yard area for Dirk Kuyt.
Turnbull comfortably beat away an early Dirk Kuyt drive, but was then helped out by a number of last-ditch tackles and blocks that frustrated Liverpool.
Gerrard fed Dirk Kuyt and the Dutchman surged at retreating defenders before drilling the ball past Kiely from the edge of the box.
Ryan Babel set up Dirk Kuyt to put the Reds ahead and only some super saves by Luke Steele kept Barnsley in the game.
Liverpool went behind to a deflected strike from former striker Craig Bellamy on Sunday before Dirk Kuyt rescued a point with a late strike.
As Liverpool pressed even more, Gerrard went close with a drive, while Dirk Kuyt - not at his best throughout the evening - shot tamely.
On the hour, Caleb Folan was sent-off for kicking out at Martin Skrtel, whose mis-timed shot was headed in by Dirk Kuyt to make it 2-0.
Steven Gerrard's cross flew it to make it 4-1 before Ryan Babel tapped in Dirk Kuyt's cross and then unknowingly deflected in Albert Riera's late shot.
Their goal was very well made by Steven Gerrard, who went past two or three players before cutting the ball back for Dirk Kuyt to score.
Substitute Dirk Kuyt looked to have given Liverpool victory in extra time, but a late Ben Turner goal sent the match into a dramatic penalty shoot-out.
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Things did not improve after the break until Crouch's goal finally broke the deadlock, just as the striker was about to be replaced by Dirk Kuyt.
His first chance fell in the 16th minute when Dirk Kuyt threaded a pinpoint through-ball, but the striker was denied by a fine sprawling save from Kirkland.
Dirk Kuyt squared a dangerous ball into the six-yard box and Israeli Benayoun slid home his fourth goal from seven games, as three defenders stood and watched.
Riise's late blunder at Anfield in the 95th minute changed the complexion of the tie after Dirk Kuyt had put the Reds ahead in the first half.
Gerrard produced a wonderful piece of magic on the right to find Dirk Kuyt who poked in for 3-0 before substitute David Ngog nodded in in injury time.
Steven Gerrard robbed Shelton Martis before dinking the ball in for the first, with Dirk Kuyt driving home a shot in the second half to make it 2-0.
In their next attack, Robben made it 3-1, escaping the attentions of Diego Godin to meet Dirk Kuyt's cross and plant a firm header into the bottom corner.
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