Rooney and Mata both found the net before half-time, the latter apparently from an offside position, before van Persie added a third to avenge United’s loss to Liverpool by the same scoreline at Old Trafford in March.
Victory, United’s sixth in a row, allowed Louis van Gaal’s side to move back to within eight points of leaders Chelsea and five of champions Manchester City, fuelling hopes of a slow-burning title push.
“I think we have scored wonderful goals,” United manager van Gaal told Sky Sports.
“In spite of the goals, we gave a lot of chances away. That was every time we gave unnecessary passes away and that is how we have to improve.”
United’s fans finished the game by chanting “You’re getting sacked in the morning!” at Liverpool coach Brendan Rodgers, whose side limped out of the Champions League in mid-week and now trail United by 10 points.
But Liverpool might have emerged from the game with more credit had it not been for a stunning display by United goalkeeper David de Gea, who denied Raheem Sterling and substitute Mario Balotelli three times each.
“We created so many chances today and David de Gea was man of the match,” said Rodgers.
“Today we created opportunities, which we haven’t been doing. I’ll keep searching for the solutions.”
Rodgers had reacted to the poor form of his own goalkeeper, Simon Mignolet, by dropping him in favour of Brad Jones, and the Australian’s presence on the pitch at kick-off was not the only novelty.
Both teams lined up with three-man defences, with midfielder Michael Carrick marshalling United’s back line and Liverpool full-back Glen Johnson playing in a narrower role than usual.
De Gea was presented with United’s player of the month award prior to kick-off and he demonstrated his value to van Gaal in the 12th minute by sliding out to thwart Sterling from Adam Lallana’s incisive pass.
– Johnson forced off –
Within a minute, United were ahead. Antonio Valencia left Joe Allen chasing shadows with a cute nutmeg on the right flank before cutting the ball back for the unmarked Rooney to sweep home from 15 yards.
With Rickie Lambert named on the bench alongside the fit-again Balotelli, it was left to Sterling to give Liverpool a cutting edge.
The England forward, who turned 20 this week, teed up Steven Gerrard for a low shot that De Gea saved comfortably and then left Phil Jones for dead inside the United box, only for the Spaniard to deny him at the near post.
Just as in their 2-1 win at Southampton last Monday, United had gone ahead against the run of play, and Liverpool’s cause was not helped when Johnson went off holding his groin in the 25th minute. Kolo Toure replaced him.
There was more woe to come as United inflated their lead five minutes before half-time with a goal that carried more than a hint of injustice.
Van Persie’s head made only fleeting contact with Ashley Young’s left-wing cross, but it meant that Mata, who followed in to head home at the back post, was offside. Unfortunately for Liverpool, the officials missed it.
Rodgers sent on Balotelli for Lallana at half-time, but the visitors continued to misfire in the United box.
Jordan Henderson headed over from a Sterling cross and when Jonny Evans’s careless square pass gave Sterling a free run on goal, a heavy touch took him wide and De Gea sped out to dismay him again.
Seconds later Van Persie gave Rooney a sight of goal at the other end, only for the captain to shoot tamely at Jones, while the Dutchman then prodded wide from Valencia’s drilled cross.
De Gea superbly palmed a close-range shot from Balotelli onto the crossbar to leave Rodgers ruing his luck again and in the 71st minute it was all over.
Dejan Lovren did not get enough purchase on his attempt to clear Rooney’s low cross and Mata cleverly teed up Van Persie to brush home his fourth goal in four games.
Still De Gea stood firm, saving twice from Balotelli in the latter stages, while Jones tipped a shot from Van Persie over the bar.