Jonjo Shelvey was issued a straight red card near the end of the first half for a challenge on Jonny Evans; however, Steven Gerrard volleyed the Reds ahead minutes after the interval.
Rafael da Silva curled home United's equaliser four minutes later before van Persie slotted from 12 yards with 10 minutes remaining.
Before the game got underway red and white coloured leaflets were raised by the Kop and sections of the Centenary and Anfield Road stands, portraying three simple yet poignant messages: "The Truth," "Justice" and "96."
To commemorate the findings of the Hillsborough Independent Panel's report, the mosaic was held as You'll Never Walk Alone rang around Anfield and remained in place for the first minute of the game.
On seven minutes, Raheem Sterling slipped a pass into the channel for Luis Suarez, who fired the ball across the face of goal. Anders Lindegaard got a hand to it and just as Gerrard stormed the penalty area to smash home the loose ball and send Anfield into ecstasy, the danger was removed.
Fabio Borini was then denied after Suarez pivoted sharply and threaded an instinctive pass between a wall of United defenders for him to chase. However, when the Italian found himself a yard clear of any marker and clean through on goal, his first touch was too heavy and Lindegaard was out quickly to smother his effort.
Roared on by the home fans the Reds looked the more dangerous of the two teams.
Gerrard side-footed into the side netting after an innocuous short free-kick fooled the United defence. Daniel Agger was bundled to the ground in the penalty area by Evans but Mark Halsey waved away the raucous appeals for a spot-kick.
Suarez slalomed towards the United goal as defenders swarmed around him in an attempt to pre-empt his next move. The Uruguayan shuffled the ball onto his right foot and tried to whip it into the top corner of Lindegaard's net but his strike dipped over the bar.
It was all Liverpool. United seemed content to defend deep and when it broke up the field, the visitor was unable to chose the killer pass, so waves of Liverpool pressure ebbed and flowed back in its direction.
However, in the 38th minute, Anfield was stunned when Shelvey launched himself into a 50-50 challenge with Evans, and Halsey deemed him to have come over the ball with two feet and the midfielder was sent off.
Deflated only momentarily, the home side refused to surrender momentum. Suarez sent a free-kick crashing towards Lindegaard's left but the 'keeper was down smartly to parry. Joe Allen fed a pass into Borini, who cut the ball back from the touchline but no Liverpool player could turn home his inviting pass.
Suso was introduced as a half-time substitute and the youngster made an immediate impact by kick-starting the move that led to the Reds' opener.
His attempted cross was blocked and Glen Johnson picked up possession. The full-back darted into the United penalty area where the ball bobbled up to Gerrard. The skipper controlled with his chest before volleying left-footed into the corner of Lindegaard's net.
Anfield was rocking but it was soon to be silenced as four minutes after Gerrard's opener, the Reds were pegged back. Rafael found a yard of space inside the Liverpool box and curled past Pepe Reina and into the top corner if his net for 1-1.
On the hour mark Suarez let the ball roll across his body as he swivelled on the edge of the penalty area and fired low towards the corner of Lindegaard's goal. Once again, however, the 'keeper was not found wanting as he palmed the ball to safety.
United crept back into the game as time wore on. Alex Ferguson's men looked more dangerous on the ball as van Persie lurked on the shoulder of the Liverpool defence.
And despite a short spell of possession for the home side, Antonio Valencia seized upon a mix-up for the Reds and ran half the length of the field before going to ground in the box.
Reina was booked, a penalty awarded and Van Persie side-footed the ball home to clinch victory for United.
Liverpoolfc.com journalists' man of the match: Steven Gerrard