Liverpool and West Ham fought out a largely disappointing goalless draw which damages the home team's European ambitions but eased relegation concerns for their opponents.
The Hammers were denied their first win at Anfield for 50 years when Lucas Leiva cleared Jack Collison's late header off the line.
Luis Suarez was marshalled expertly by West Ham defender James Collins, although the Uruguay forward did force an injury-time save from Jussi Jaaskelainen at the goalkeeper's near post with a low shot.
Liverpool were outstanding - Rodgers
The draw leaves Liverpool in seventh, three points behind local rivals Everton having played an extra match, while West Ham are now seven points clear of the relegation zone.
It also brings the east London side to within a point of the
manager Sam Allardyce has set before he signs a new contract with the Upton Park club.
The central-defensive pairing of Collins and James Tomkins were crucial to securing their side's clean sheet, as Allardyce earned a first point in his last nine games against the Reds.
The match had been preceded by a minute's silence in the last game at Anfield before the 24th anniversary of the Hillsborough disaster on 15 April.
When the action got under way, Liverpool had the majority of possession and looked the more threatening going forward, without creating any clear-cut chances.
Ian DennisBBC Match of the Day commentator
"West Ham have got a precious point in their bid to secure survival but Liverpool have dropped points in their challenge for a European place. A deserved draw for Hammers boss Sam Allardyce's side and a frustrating result for Reds counterpart Brendan Rodgers."
And it was the visitors who went close to taking the lead when midfielder Mohamed Diame, showing sparks of his quality, beat four Liverpool defenders inside the box before hammering a strike over the bar.
Liverpool's frustrations increased when Daniel Sturridge, who replaced Stewart Downing midway through the first half, saw his shot on the turn saved at the far post on the stroke of half-time.
After the break, the Merseysiders increased the pressure but the visitors held firm, Tomkins blocking a goal-bound Steven Gerrard effort just in front of the line.
The home side did have the ball in the net when Sturridge turned in Jordan Henderson's shot only for the goal to be disallowed for offside.
West Ham thought they should have had a penalty for a Jose Enrique tackle on Tomkins, who then might have conceded a spot-kick himself for a challenge on Gerrard.
Hammers had best chances - Allardyce
As Liverpool continued to struggle to find a way through the visitors, West Ham almost stole the three points late on but Lucas cleared Collison's header off the goal-line.
Liverpool boss Brendan Rodgers:
"The effort the players put in was very good. We just needed a bit of luck to go our way. I'm disappointed Daniel Sturridge's goal was disallowed for offside as I thought it was onside.
"You have to give West Ham credit as they defended very well. I never for one moment thought they were going to win it. They got in some great blocks and are an honest group of players that put their bodies on the line but only one team tried to win it and that was us, but we couldn't put the ball in the back of the net."
West Ham manager Sam Allardyce:
"I am content, even though we should have won the game. We nullified Liverpool's strengths and created the better chances to score. I'm delighted. It's only our finishing that has cost us the three points.
"Jose Enrique kicked James Tomkins when we should have had a penalty but I am satisfied with the performance and result. We know we've created better chances than Liverpool, even though they had more possession.
"James Collins and James Tomkins were outstanding. It's a big point. We are ever closer to the magic 40."
Full Time The referee blows his whistle to end the game.
Gary O'Neil challenges Oussama Assaidi unfairly and gives away a free kick. Leiva Lucas takes the free kick.
Luis Suarez takes a shot. Save by Jussi Jaaskelainen. Corner from left by-line taken by Luis Suarez.
Free kick awarded for an unfair challenge on Matthew Jarvis by Oussama Assaidi. Direct free kick taken by Matthew Taylor.
Unfair challenge on Leiva Lucas by Carlton Cole results in a free kick. Steven Gerrard restarts play with the free kick.
Oussama Assaidi crosses the ball, clearance made by James Collins.
Matthew Taylor produces a cross.
Oussama Assaidi has an effort at goal from outside the penalty area missing to the wide left of the goal.
Inswinging corner taken right-footed by Gary O'Neil from the left by-line, Jack Collison takes a shot. Leiva Lucas manages to make a clearance.
Booking The referee shows Joey O'Brien a yellow card.
Oussama Assaidi produces a cross.
Outswinging corner taken by Luis Suarez from the right by-line, clearance made by Jack Collison.
Substitution (West Ham) makes a substitution, with Emanuel Pogatetz coming on for James Tomkins.
Effort from 30 yards by Daniel Agger. Save made by Jussi Jaaskelainen.
A cross is delivered by Matthew Jarvis, Sanchez Jose Enrique makes a clearance.
Jack Collison is adjudged to have handled the ball. Free kick taken by Leiva Lucas.
Daniel Sturridge takes a shot. Jussi Jaaskelainen makes a save.
Mohamed Diame delivers the ball, Jose Reina makes a comfortable save.
Matthew Taylor takes a shot. Blocked by Jamie Carragher.
Steven Gerrard produces a right-footed shot from just outside the penalty area that goes harmlessly over the target.
Matthew Jarvis concedes a free kick for a foul on Jamie Carragher. Free kick taken by Jose Reina.
Substitution Oussama Assaidi replaces Jordan Henderson.
Corner taken by Phillippe Coutinho from the right by-line to the near post, Effort from deep inside the area by Daniel Sturridge misses to the right of the goal.
Phillippe Coutinho takes a shot. Blocked by James Collins. Corner taken right-footed by Steven Gerrard, clearance made by James Collins. Effort from outside the box by Luis Suarez goes wide right of the target.
Matthew Taylor takes a shot. Glen Johnson gets a block in.
Foul by Steven Gerrard on Gary O'Neil, free kick awarded. Direct free kick taken by Jussi Jaaskelainen.
Phillippe Coutinho takes the inswinging corner, clearance made by Joey O'Brien.
Daniel Sturridge is caught offside. Jussi Jaaskelainen takes the free kick.
Matthew Taylor sends in a cross, Headed effort from deep inside the area by Mohamed Diame misses to the right of the goal.
Free kick crossed right-footed by Gary O'Neil from left wing.
Substitution Ricardo Vaz Te goes off and Jack Collison comes on.
Substitution Matthew Taylor joins the action as a substitute, replacing Kevin Nolan.
Foul by Jordan Henderson on Joey O'Brien, free kick awarded.
Luis Suarez produces a drilled right-footed shot from deep inside the penalty area which goes wide of the left-hand post.
Luis Suarez produces a cross.
The ball is swung over by Matthew Jarvis.
Phillippe Coutinho is ruled offside. Free kick taken by Jussi Jaaskelainen.
Steven Gerrard takes a shot. James Tomkins gets a block in.
The ball is crossed by Steven Gerrard, James Collins makes a clearance. Phillippe Coutinho decides to take the corner short.
A cross is delivered by Carlton Cole, clearance made by Daniel Agger.
Free kick awarded for an unfair challenge on James Tomkins by Leiva Lucas. James Collins takes the free kick.
Gary O'Neil fouled by Jamie Carragher, the ref awards a free kick. Direct free kick taken by Jussi Jaaskelainen.
Daniel Agger takes a shot. Blocked by James Collins. Short corner taken by Luis Suarez from the right by-line.
Centre by Jamie Carragher, clearance made by Joey O'Brien. Outswinging corner taken by Steven Gerrard from the right by-line, clearance by Joey O'Brien.
The ball is swung over by Daniel Sturridge, clearance made by James Tomkins.
The referee gets the second half underway.
45:00 +1:09 Half time
Half Time The referee calls an end to the first half.
Luis Suarez takes the inswinging corner, Daniel Sturridge takes a shot. Save made by Jussi Jaaskelainen.
Jordan Henderson takes a shot. Blocked by James Tomkins. Inswinging corner taken right-footed by Phillippe Coutinho, Kevin Nolan manages to make a clearance.
A cross is delivered by Joey O'Brien, Header from close in by Kevin Nolan misses to the left of the target.
The ball is delivered by Matthew Jarvis, Headed effort from close range by Carlton Cole goes wide left of the goal.
Foul by Leiva Lucas on Ricardo Vaz Te, free kick awarded. Direct free kick taken by Jussi Jaaskelainen.
Short corner taken by Steven Gerrard from the right by-line.
Pass corner from left by-line taken by Steven Gerrard to short.
Carlton Cole takes a shot. Blocked by Daniel Agger.
Kevin Nolan gives away a free kick for an unfair challenge on Steven Gerrard. Jamie Carragher takes the direct free kick.
Daniel Sturridge challenges Joey O'Brien unfairly and gives away a free kick. James Collins takes the free kick.
Luis Suarez takes a shot. Save made by Jussi Jaaskelainen.
Phillippe Coutinho is flagged offside by the assistant referee. Indirect free kick taken by Jussi Jaaskelainen.
Substitution Daniel Sturridge comes on in place of Stewart Downing.
Shot by Mohamed Diame from deep inside the six-yard box clear the bar.
Outswinging corner taken right-footed by Gary O'Neil from the right by-line to the near post, clearance by Jamie Carragher.
Stewart Downing takes a shot. Jussi Jaaskelainen makes a save.
Long range shot from Luis Suarez misses to the left of the target.
Matthew Jarvis produces a cross, save by Jose Reina.
Effort on goal by Mohamed Diame from long range goes harmlessly over the bar.
Mohamed Diame crosses the ball, Ricardo Vaz Te has a headed effort at goal from deep inside the area missing to the right of the target.
Effort from 25 yards by Phillippe Coutinho. Blocked by James Collins.
Kevin Nolan crosses the ball.
Steven Gerrard produces a right-footed shot from just outside the box that goes wide left of the target.
Phillippe Coutinho takes the chance to get an effort at goal. Save made by Jussi Jaaskelainen.
Phillippe Coutinho is ruled offside. Free kick taken by Jussi Jaaskelainen.
Foul by Leiva Lucas on Gary O'Neil, free kick awarded. Gary O'Neil delivers the ball from the free kick right-footed from right channel, save by Jose Reina.
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