Midfielder Yossi Benayoun and forwards Gael Kakuta and Salomon Kalou suffered problems in Chelsea's 4-3 loss.
Benayoun teed up an early chance for Rodriguez but his shot was easily saved by Green.
Gordon saved from Yossi Benayoun and debutant Robbie Keane unintentionally blocked Torres' shot before his winner.
Benitez looked concerned as Lille grew more confident and introduced Yossi Benayoun for the tiring Babel.
Yossi Benayoun should have done better than head the loose ball tamely at Edwin van der Sar.
Yossi Benayoun scored the Reds' winner when he headed in a Fabio Aurelio free-kick from eight yards.
Yossi Benayoun slotted in a second to secure the win after keeper Marton Fulop had spilled Ngog's cross.
It took a moment of individual brilliance from Benayoun to break the deadlock 15 minutes from full time.
Midfielder Yossi Benayoun has added to the uncertainty around the club by admitting he is unsure of his future.
England forward Theo Walcott and Israel midfielder Yossi Benayoun grabbed the other goals.
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It got worse when Benayoun's cross was only cleared to Skrtel, whose shot was diverted past keeper Myhill by Kuyt's header.
Yossi Benayoun slid a delightful ball into striker Anelka, who put a ball across which Essien side-footed in from 12 yards.
Seconds after the restart, Benayoun put West Ham ahead with an exquisite chip and it appeared the hosts would overpower their opponents.
El Zhar follows Steven Gerrard, Fernando Torres, Dirk Kuyt, Yossi Benayoun and Daniel Agger in committing his long-term future to the club.
Liverpool's wide players, Yossi Benayoun and Ryan Babel, also found the going tough - as did Blackburn's wingers Morten Gamst Pedersen and Bentley.
Yossi Benayoun's 82nd minute header was enough to hand the Reds victory in the first leg of the last-16 tie at the Bernabeu.
Sunderland tried to muster a response but struggled retain possession before Fulop's error from Ngog's hooked cross allowed a grateful Benayoun to slot home.
He mis-hit his shot, but it lofted invitingly into the path of Benayoun, who headed straight at Van der Sar from only six yards.
We changed some players and it was very, very positive to see Crouch play well, Yossi Benayoun playing and Damien Plessis make his debut.
Admir Vladavic had two long-range strikes for Zilina blocked away by Cech but their predicament got worse when Benayoun played another telling ball from midfield.
And Liverpool threw everything at the visitors, forcing Steele into another smart stop from Benayoun before he tipped a Lucas header on to the bar.
At half-time Liverpool manager Rafa Benitez tweaked his formation to a 4-3-3, pushing Babel closer to the front two and freeing Yossi Benayoun in midfield.
However, when Benayoun took advantage of some sloppy defending and kept his feet after rounding the keeper to poke home, it seem the result was set.
They were, however, unfortunate not to level when Yossi Benayoun beat Atletico goalkeeper David de Dea - but his effort was wrongly ruled out for offside.
Israel playmaker Benayoun revealed that, despite signing a two-year contract extension last summer, he may be one of those heading out of the club this summer.
Benayoun jinked his way into the area and dragged a scuffed pass to his captain, and the England midfielder duly took advantage with a low finish.
On the same day 12 months ago, a Yossi Benayoun goal saw the Reds claim a famous away win in the Champions League against Real Madrid.
Torres dribbled around Boaz Myhill to restore the Reds' lead and rolled in to complete his treble after latching on to a clever Yossi Benayoun pass.
However, Real Madrid target Xabi Alonso and Israeli star Yossi Benayoun successfully came through training after recovering from ankle injuries and will be available to play.
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.
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