Liverpool again wasted a chance to take a commanding lead at the top of the English Premier League as brave West Ham produced a minor miracle of its own to leave Anfield with a 0-0 draw.
It is 45 years since it has won at the stadium, so this first point in nine years at Liverpool was a fine achievement.
West Ham has never been known for its defensive reliability at Liverpool, but it was magnificent as it stretched an unbeaten run to three games.
At the back goalkeeper Robert Green, England defender Matthew Upson and Welshman James Collins stood defiant.
And another Welshman, former Liverpool man Craig Bellamy, came close to breaking the deadlock with a 30-yard shot which crashed against a post.
Liverpool is back on top of the table, but by only one point, and this disappointing display follows hot on the heels of an identical result achieved by Fulham at Anfield in the previous home league game.
Liverpool dominated, but West Ham repelled the waves of attacks as it grabbed a crucial point in its own battle for survival.
Liverpool called in veteran defender Sami Hyypia and former West Ham winger Yossi Benayoun, keen to take advantage of Chelsea's defeat by Arsenal 24 hours earlier.
Robbie Keane and Andrea Dossena replaced the injured pair Fernando Torres and Fabio Aurelio, with Daniel Agger and Javier Mascherano rested to the bench.
West Ham, without a win at Anfield since 1963, brought in Hayden Mullins in midfield for ankle injury victim Lee Bowyer, in the only change from the side that won at Sunderland last time out.
Mark Noble returned to the Hammers bench after a knee injury, while Diego Tristan made his first appearance in the squad since he joined on trial two months ago.
Liverpool had two early penalty appeals turned down by referee Peter Walton when both Benayoun and then Dirk Kuyt drove the ball at Herita Ilunga from close range.
West Ham had looked nervy, and after 14 minutes Green raced from his line to punch weakly away. The ball fell to Albert Riera whose shot was blocked in the six-yard box by James Collins.
Then from a right-wing corner, Hyypia rose to head narrowly over the bar. The Liverpool pressure increased and Mullins was booked after 19 minutes when he tripped Benayoun in full flow.
Two minutes later another header from Hyypia was kicked off the line by Ilunga.
West Ham's only shot until this point had been a weak long-range effort from Julien Faubert, scooped up by Jose Reina.
But Liverpool kept plugging away, showing the sort of patience in such situations that Benitez called for after the stalemate against Fulham nine days earlier.
Steven Gerrard worked his way in from the right and fired into the sidenetting, before Bellamy - on his return to Anfield after moving to West Ham 17 months ago - almost broke the deadlock.
Bellamy picked up possession and unleashed a fine, swerving drive which crashed against Reina's right-hand post and bounced across goal to safety.
Then Green made a fine point-blank save from Kuyt's header following Xabi Alonso's corner, two minutes from the break.
Kuyt and Keane both saw shots go wide as Liverpool opened the second half on the attack. But Bellamy was still a danger for West Ham, and after running past Hyypia he was body-checked by Alonso, the Spaniard being booked.
Then Green produced a