Van Persie makes Liverpool pay penalty
The Dutchman's goal saw United complete a come from behind victory after Rafael da Silva's effort had cancelled out Liverpool captain Steven Gerrard's volley early in the second half.
Victory saw United move to within a point of Premier League leaders Chelsea but left Liverpool, who saw Jonjo Shelvey sent off in the 39th minute, still searching for their first league win under manager Brendan Rodgers.
Talk before the game was about whether Liverpool's Luis Suarez and United's Patrice Evra would shake hands following the Uruguay striker's refusal to do so last season after his eight-game ban for racially abusing the defender.
But Suarez did shake his foe's hand ahead of Liverpool's first home match since an independent report cleared the Merseysiders' supporters of any involvement in the deaths of 96 fans during the 1989 Hillsborough disaster.
United defender Nemanja Vidic was rested by manager Alex Ferguson with Jonny Evans keeping his place from their 1-0 Champions League win over Galatasaray and Rio Ferdinand returning after missing the victory over the Turkish side.
Both Ferguson and Rodgers had pleaded with their respective supporters to abandon chants mocking both Hillsborough and the 1958 Munich air disaster, which killed several United players, that had often marred previous meetings between English football's two most successful clubs.
By and large their wishes were respected, although there was a chant of "where's your famous Munich song?" from some United fans.
Liverpool soon settled and a Suarez cross was not dealt with convincingly by Anders Lindegaard, who returned to the side following rival United goalkeeper David de Gea's appearance in midweek.
Gerrard had a much better chance moments later, but his low strike from Shelvey's corner clipped the post.
Liverpool, in control without creating many clear-cut chances, suffered a huge setback when Shelvey was sent off by referee Mark Halsey for a two-footed lunge on United defender Evans.
That did not stop Liverpool getting forward, however, and they scored just after the break when Scholes, on at half-time for the ineffective Nani, challenged Glen Johnson and the ball fell to Gerrard.
The Liverpool skipper chested it down before volleying past Lindegaard in the 46th minute to the delight of the Anfield faithful.
But United were level five minutes later when, after good build-up work by Antonio Valencia and Shinji Kagawa, Rafael's curler gave Liverpool goalkeeper Pepe Reina no chance.
Suarez had a penalty shout in the 56th minute when Evans challenged him in the area but Halsey waved away protests and did so again when Scholes went in strongly on Raheem Sterling.
Just after the hour mark, Suarez's low strike forced Lindegaard into a superb stop before United took the lead against the run of play.
Valencia burst clear from midfield and, with Liverpool short at the back because Martin Skrtel was down with an injury, Johnson panicked and barged through the back of the midfielder to concede the spot kick in the 78th minute.
United had missed their last three penalties, however, so the pressure was on van Persie, one of those who had been off-target from the spot along with Nani and Javier Hernandez.
But this time the striker calmly shot into the corner, despite Reina getting fingertips to the ball, as United secured their first win at Anfield since 2007.
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