Dirk Kuyt's late strike earned Liverpool a dramatic victory over Manchester United in the FA Cup fourth round at Anfield.The tie seemed destined for a replay at Old Trafford as Ji-Sung Park's powerful shot put United level after Daniel Agger had headed Liverpool into the lead - but there was a late twist to a surprisingly flat encounter.Liverpool substitute Kuyt escaped the attentions of Patrice Evra with two minutes left to latch on to Andy Carroll's flick and fire past United goalkeeper David de Gea in front of an ecstatic Kop.It capped a perfect four days for Liverpool and manager Kenny Dalglish after reaching the Carling Cup final and their first Wembley appearance since 1996 at the expense of Manchester City on Wednesday, then sending their fierce rivals out of the FA Cup to reach the last 16.The backdrop to the game was the incident involving Liverpool's Luis Suarez and Evra in the Premier League game at Anfield in October that led to the Uruguayan being banned for eight games by the Football Association for racially abusing the United defender.And despite pleas for calm, Evra was jeered loudly by Liverpool's supporters every time he gained possession.United have now failed to win at Anfield since 2007 and manager Sir Alex Ferguson saw a gamble on keeper De Gea fail to reap dividends as the young Spaniard endured a desperate afternoon.He failed to command his area for Agger's opener then brought pressure on United in the second half with his inability to complete a simple clearance in his area and mishandling that did nothing to ease mounting Liverpool pressure.United were without Wayne Rooney as he recovered from knee and ankle injuries while De Gea was restored in goal with Anders Lindegaard dropping to the bench.De Gea was in action in the third minute as he dived to his right to turn away Maxi Rodriguez's low shot as Liverpool attempted to take control early on.It was United, however, who dominated possession with Paul Scholes the orchestrator of a game that was played at a tempo that suited Ferguson's side.Ryan Giggs tested Reina with a low shot and the dangerous Antonio Valencia struck the outside of an upright - but it was Liverpool who took the lead after 21 minutes.United keeper De Gea was unable to make his presence felt in the company of Carroll at Steven Gerrard's corner, allowing Agger to take advantage of the uncertainty to head home.Liverpool went into retreat after scoring, allowing United to enjoy a lengthy spell of possession that concluded with Park's leveller six minutes before the interval.Jose Enrique should have dealt with a ball into the corner, but he hesitated and allowed Rafael to cross for Park to thump a powerful finish into the bottom corner beyond Liverpool keeper Pepe Reina, who had no chance.Martin Skrtel had to be alert after the restart to rescue Liverpool after Danny Welbeck flicked a pass past Reina towards an unguarded goal.Liverpool were being offered hope by the uncertainty of United keeper De Gea, who put his defence under pressure when he failed to complete a simple clearance then allowed a cross to slip through his hands to needlessly concede a corner.Dalglish then used his substitutes in quick succession, sending on Charlie Adam and Kuyt for Maxi and Jamie Carragher before throwing Craig Bellamy into the fray in place of tiring captain Gerrard with 18 minutes left.It prompted Ferguson to make a change of his own as Javier Hernandez took the place of Scholes, who had barely wasted a pass in any area of the pitch.In his absence Liverpool were able to push United back towards their own goal and the winning strike came with two minutes left.Reina's clearance was flicked on by Carroll and Evra lost Kuyt, allowing the striker to beat De Gea with a low shot in front an exultant Kop.