By Phil McNultyBBC Sport chief football writer at Anfield
Robin van Persie's late penalty gave Manchester United victory over Liverpool on a poignant afternoon at Anfield.
On an occasion when the Hillsborough victims and families were remembered in moving scenes before kick-off, these two great rivals produced a typically competitive and contentious encounter.
Liverpool were reduced to 10 men when Jonjo Shelvey was sent off for a first-half foul on United defender Jonny Evans - but it did not stop captain Steven Gerrard volleying them ahead seconds after the interval.
Red card disappoints Rodgers
United, barely in the game for long periods, responded with a spectacular equaliser from Rafael Da Silva before Van Persie confirmed a fourth straight Premier League win nine minutes from time after Glen Johnson fouled Antonio Valencia.
It left Liverpool and new manager Brendan Rodgers without a league win in five attempts this season and in the Premier League's bottom three, once again rueing their lack of cutting edge.
Liverpool enjoyed spells of complete domination in territory and possession but failed to make it count, leaving United, who were without centre-back Nemanja Vidic, the opportunity to take full advantage for their first win at Anfield in six games.
The panel cleared Liverpool's supporters of blame and the build-up to kick-off was marked with a series of tributes to commemorate the occasion.
Phil McNultyChief football writer, BBC Sport
"The occasion had been impeccably observed by both clubs and by both sets of supporters until the game's conclusion.
"With the stadium virtually deserted except for the Manchester United supporters kept back in their section of the Anfield Road end, there was a brief outbreak of the chant 'Always the victims - it's never your fault'.
"It ended after a few seconds with unconfirmed reports that it was prompted by some provocation.
"The United fans were then kept back for another short period before being allowed to leave Anfield.
"It provided a blot on what was an otherwise solemn and dignified occasion but should not detract from so much of what else went on during a day when the Hillsborough families and victims were remembered."
Supporters arrived hours before the start to lay floral tributes at Anfield's Eternal Flame Hillsborough memorial and The Kop was emblazoned with a mosaic reading "The Truth" while the word "Justice" decorated the lower Centenary Stand.
Manchester United legend Sir Bobby Charlton then presented flowers to Liverpool's record goalscorer Ian Rush as opposing captains Gerrard and Ryan Giggs released 96 red balloons in memory of those who lost their lives.
There was no repeat of last season's scene at Old Trafford when the Uruguayan, who had been found guilty of racially abusing the United defender, refused the Frenchman's hand.
When the action did start Liverpool exerted complete control of the first half but could not find the finishing touch to compliment their fine approach work. Gerrard was closest with a shot narrowly off target at the near post as United struggled to find any fluency.
Liverpool's flow was disrupted in the 39th minute when they lost Shelvey as he was shown a straight red card by referee Mark Halsey for a reckless lunge at Evans that left the United defender requiring treatment.
Rodgers replaced Fabio Borini with Suso at the start of the second half and he was instantly involved as Liverpool claimed the lead they deserved. He showed confidence on the flanks and the move, which also included clever work from Johnson, ended with Gerrard sweeping a left-foot volley past Anders Lindegaard in front of an ecstatic Kop.
United, who had brought Paul Scholes on for Nani to provide a measure of order to their midfield, were quickly level as Shinji Kagawa chested Valencia's cross into the path of Rafael, who curled a superb finish beyond the stretching Pepe Reina.
Liverpool were still pressing forward and twice Lindegaard rescued United, saving low from Suarez then turning Suso's rising shot over the top.
Ferguson says Man Utd were 'very poor'
United had stabilised after that poor first half but it was still against the run of play when they went ahead from the spot - and Liverpool's undoing was all their own work.
Daniel Agger and Johnson collided on the halfway line to concede possession, allowing Valencia to race forward. The run ended with Johnson upending the winger in a desperate attempt at recovery.
To make matters worse for the home side, Agger was hurt in the clash was taken off on a stretcher before Van Persie finally converted the penalty, despite Reina getting a hand to his powerful effort which found the top corner.
Liverpool had run out of steam, ending with nine men after Martin Kelly was injured, allowing United to close out an important win.
The ball is crossed by Steven Gerrard, save by Anders Lindegaard.
Danny Welbeck fouled by Jesus Fernandez Saez, the ref awards a free kick. Paul Scholes takes the free kick.
Javier Hernandez takes a shot. Save made by Jose Reina.
Free kick awarded for an unfair challenge on Martin Kelly by Ryan Giggs. Jose Reina takes the free kick.
Unfair challenge on Jonathan Evans by Jordan Henderson results in a free kick. Jonathan Evans restarts play with the free kick.
Jesus Fernandez Saez challenges Michael Carrick unfairly and gives away a free kick. Antonio Valencia takes the free kick.
Ryan Giggs takes a short corner.
The ball is swung over by Patrice Evra.
Patrice Evra takes the direct free kick.
Substitution Rafael Da Silva goes off and Danny Welbeck comes on.
Martin Kelly gives away a free kick for an unfair challenge on Jonathan Evans.
Free kick awarded for a foul by Luis Suarez on Rio Ferdinand. Anders Lindegaard takes the direct free kick.
Corner taken by Jesus Fernandez Saez from the left by-line played to the near post, clearance made by Robin van Persie.
Booking Robin van Persie receives a caution.
Glen Johnson delivers the ball, clearance by Rio Ferdinand.
Glen Johnson delivers the ball, Martin Kelly has a headed effort at goal from close in which goes wide right of the goal.
Antonio Valencia crosses the ball, clearance made by Steven Gerrard.
Substitution Javier Hernandez joins the action as a substitute, replacing Shinji Kagawa.
Assist by Antonio Valencia.
80:11 Goal scored
Goal - Robin van Persie - Liverpool 1 - 2 Man Utd Robin van Persie scores a power penalty. Liverpool 1-2 Man Utd.
Substitution Jamie Carragher is brought on as a substitute for Daniel Agger.
Booking Jose Reina receives a yellow card.
Glen Johnson challenges Antonio Valencia unfairly and gives away a Penalty.
A cross is delivered by Martin Kelly, Rio Ferdinand manages to make a clearance.
Foul by Michael Carrick on Joe Allen, free kick awarded. The free kick is delivered right-footed by Steven Gerrard from left wing, save by Anders Lindegaard.
A cross is delivered by Luis Suarez.
Substitution Raheem Sterling goes off and Jordan Henderson comes on.
Jesus Fernandez Saez takes the chance to get an effort at goal. Save by Anders Lindegaard. Steven Gerrard takes a corner.
The official flags Ryan Giggs offside. Free kick taken by Daniel Agger.
The ball is swung over by Michael Carrick, Robin van Persie produces a header from inside the area that goes over the bar.
The ball is swung over by Michael Carrick, Martin Kelly makes a clearance. Outswinging corner taken from the left by-line by Ryan Giggs, Glen Johnson manages to make a clearance. The ball is swung over by Rio Ferdinand, clearance made by Raheem Sterling.
Luis Suarez takes a shot. Save made by Anders Lindegaard.
Patrice Evra crosses the ball, clearance by Glen Johnson.
Martin Skrtel takes the free kick.
Booking The referee cautions Paul Scholes for unsporting behaviour.
Unfair challenge on Raheem Sterling by Paul Scholes results in a free kick.
Glen Johnson produces a cross, clearance by Patrice Evra.
Foul by Daniel Agger on Robin van Persie, free kick awarded. Paul Scholes restarts play with the free kick.
Steven Gerrard takes a shot. Save made by Anders Lindegaard.
The ball is delivered by Raheem Sterling, Rio Ferdinand manages to make a clearance.
Inswinging corner taken left-footed by Robin van Persie from the right by-line to the near post, Headed effort from deep inside the penalty area by Antonio Valencia goes harmlessly over the crossbar.
Shinji Kagawa provided the assist for the goal.
50:29 Goal scored
Goal - Rafael Da Silva - Liverpool 1 - 1 Man Utd Rafael Da Silva scores a goal from deep inside the penalty box to the top left corner of the goal. Liverpool 1-1 Man Utd.
Centre by Antonio Valencia.
Robin van Persie crosses the ball, clearance by Glen Johnson.
Shinji Kagawa takes a shot. Blocked by Martin Skrtel.
Patrice Evra sends in a cross, Glen Johnson manages to make a clearance.
Antonio Valencia concedes a free kick for a foul on Steven Gerrard. Joe Allen restarts play with the free kick.
Assist on the goal came from Glen Johnson.
45:49 Goal scored
Goal - Steven Gerrard - Liverpool 1 - 0 Man Utd Goal scored by Steven Gerrard from deep inside the penalty box to the bottom right corner of the goal. Liverpool 1-0 Man Utd.
Jesus Fernandez Saez delivers the ball, Rio Ferdinand makes a clearance.
The referee blows his whistle to start the second half.
Substitution Fabio Borini leaves the field to be replaced by Jesus Fernandez Saez.
Substitution Paul Scholes on for Luis Nani.
45:00 +2:12 Half time
Half Time The whistle is blown to end the first half.
The ball is swung over by Martin Kelly, clearance made by Jonathan Evans.
The ball is sent over by Fabio Borini, Patrice Evra makes a clearance. Outswinging corner taken right-footed by Steven Gerrard, Headed effort from inside the area by Daniel Agger misses to the left of the target.
Rafael Da Silva crosses the ball.
Michael Carrick takes a shot. Blocked by Martin Skrtel.
The ball is crossed by Luis Nani, clearance made by Daniel Agger.
Rio Ferdinand concedes a free kick for a foul on Luis Suarez. Luis Suarez has a direct shot on goal from the free kick, save made by Anders Lindegaard.
Rio Ferdinand gives away a free kick for an unfair challenge on Luis Suarez. Luis Suarez has a direct shot on goal from the free kick, save by Anders Lindegaard.
Direct free kick taken by Michael Carrick.
Dismissal Jonjo Shelvey sent from the field by the ref for serious foul play.
Jonathan Evans fouled by Jonjo Shelvey, the ref awards a free kick.
Daniel Agger fouled by Antonio Valencia, the ref awards a free kick. Jonjo Shelvey takes the free kick.
Martin Kelly produces a cross, Jonathan Evans makes a clearance. Raheem Sterling takes a shot. Jonathan Evans gets a block in.
Free kick awarded for an unfair challenge on Shinji Kagawa by Steven Gerrard. Direct free kick taken by Rafael Da Silva.
Martin Kelly sends in a cross, Rio Ferdinand manages to make a clearance.
Luis Suarez takes a shot. Blocked by Rio Ferdinand. Inswinging corner taken from the left by-line by Steven Gerrard.
Patrice Evra concedes a free kick for a foul on Raheem Sterling. Steven Gerrard sends in a cross, Headed effort from inside the box by Luis Suarez misses to the right of the target.
Patrice Evra produces a cross, clearance made by Martin Skrtel.
Joe Allen concedes a free kick for a foul on Shinji Kagawa. Rio Ferdinand takes the direct free kick.
Luis Suarez produces a right-footed shot from just outside the box that misses to the right of the net.
Unfair challenge on Shinji Kagawa by Martin Kelly results in a free kick. Shot comes in from Luis Nani from the free kick.
The ball is swung over by Steven Gerrard, save by Anders Lindegaard.
Centre by Martin Kelly, clearance by Rafael Da Silva. Corner taken by Steven Gerrard from the left by-line played to the near post, clearance made by Robin van Persie.
Martin Kelly sends in a cross, Jonathan Evans makes a clearance.
Jonjo Shelvey gives away a free kick for an unfair challenge on Rafael Da Silva. Rio Ferdinand restarts play with the free kick.
Fabio Borini crosses the ball, clearance made by Rio Ferdinand.
Free kick awarded for a foul by Fabio Borini on Shinji Kagawa. Rio Ferdinand restarts play with the free kick.
Raheem Sterling delivers the ball, Rafael Da Silva manages to make a clearance. Short corner taken by Jonjo Shelvey from the right by-line, Effort from deep inside the area by Steven Gerrard misses to the right of the goal.
Luis Suarez takes a shot. Jonathan Evans manages to make a clearance.
Ryan Giggs produces a left-footed shot from just outside the box that misses to the right of the target.
Corner crossed in by Steven Gerrard, clearance by Rafael Da Silva.
Patrice Evra crosses the ball, Daniel Agger manages to make a clearance.
Free kick awarded for a foul by Daniel Agger on Robin van Persie. Free kick taken by Ryan Giggs.
The game kicks-off.
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