The Holland international continued his remarkable scoring spree with a close-range effort in the first half which was doubled after the break by Nemanja Vidic.
Liverpool substitute Daniel Sturridge overshadowed team-mate Luis Suarez, who began the day one behind Van Persie on 15 top-flight goals for the season, by marking his league debut for his new club with a second goal in as many matches and had a chance to snatch a point late on, but United held on grimly, if somewhat unconvincingly.
In it goes: Nemanja Vidic claimed the decisive goal after the ball brushed off his head before finding the net
Cruising: Manchester United went 2-0 up after Nemanja Vidic scored off Patrice Evra's (left) header
Back on: Substitute Daniel Sturridge pulled a goal back for the visitors to make it 2-1
MATCH FACTS
Man Utd: De Gea, Da Silva, Ferdinand, Vidic (Smalling 79), Evra, Carrick, Cleverley, Young (Valencia 46), Kagawa (Jones 77), Welbeck, Van Persie
Subs: Amos, Anderson, Giggs, Hernandez
Goals: Van Persie 19, Vidic 54
Booked: Evra
Liverpool: Reina, Wisdom, Skrtel, Agger, Johnson, Lucas (Sturridge 46), Downing, Gerrard, Allen (Henderson 80), Sterling (Borini 62), Suarez
Subs: Jones, Carragher, Shelvey, Robinson
Goal: Sturridge 57
Booked: Allen, Skrtel, Johnson, Agger
Referee: Howard Webb (S Yorkshire)
Attendance: 75,501
Subs: Amos, Anderson, Giggs, Hernandez
Goals: Van Persie 19, Vidic 54
Booked: Evra
Liverpool: Reina, Wisdom, Skrtel, Agger, Johnson, Lucas (Sturridge 46), Downing, Gerrard, Allen (Henderson 80), Sterling (Borini 62), Suarez
Subs: Jones, Carragher, Shelvey, Robinson
Goal: Sturridge 57
Booked: Allen, Skrtel, Johnson, Agger
Referee: Howard Webb (S Yorkshire)
Attendance: 75,501
Van Persie - expertly and clinically - scored with virtually his first chance and could have had at least one other in the first half.
Suarez toiled in vain but never got the remotest inkling of an opportunity against Rio Ferdinand and Vidic - reunited in the centre of defence for the first time since September - with his one effort coming just before the interval and only troubling the fans in the Stretford End.
In spite of the age-old rivalry between England's two most-decorated clubs the first quarter of the game was something of a non-entity.
United enjoyed the greater dominance, as was to be expected from the home team, while not creating anything too threatening while Liverpool counter-attacked sporadically but fared even worse in the final third.
It changed in the 19th minute when, with United steadily building the pressure, the ball was worked from right to left for Patrice Evra to pick up in space.
Offside? Nemanja Vidic appeared to be ahead of Evra when the ball was knocked onto him
Me again: Robin van Persie scored the opener at Old Trafford to put United 1-0 up
Lethal: Van Persie celebrated his 17th goal of the Premier League season
The statistics now adding up for the Holland international are startling. It was his 65th goal in 77 league matches, his 10th in the past 10 games, his fifth in five against Liverpool (three coming for Arsenal and the other at Anfield earlier in the season) and his 20th of the campaign.
Van Persie should probably have had another having charged through a gaping hole between centre-backs Martin Skrtel and Daniel Agger to collect Ashley Young's through-ball but he uncharacteristically ballooned over.
Liverpool, possibly due to the inexperience of the likes of Andre Wisdom, Raheem Sterling and Joe Allen, appeared to crumble.
Allen, who is so often hailed for his possession statistics, passed the ball straight to Danny Welbeck and the Wales midfielder's embarrassment was only saved by a block from Agger.
Welbeck then skipped past Skrtel to fire over while Tom Cleverley saw a left-foot volley flash just wide of Jose Reina's left-hand post.
Only a brilliant goalline clearance from Skrtel from Van Persie's clever backheel from Rafael's cross prevented a second, with Reina taking a hefty whack from Shinji Kagawa in the aftermath which required lengthy treatment.
Battle: Danny Welbeck tries to hold off Martin Skrtel (right) of Liverpool
Keeping up appearances: Jose Mourinho (right) and Roy Hodgson (left) were at Old Trafford for the match
United winger Ashley Young failed to reappear for the second half - replaced by Antonio Valencia - having injured himself after recklessly jumping into a tackle on Agger, for which he escaped any punishment.
However, the more significant introduction at the interval was that of Sturridge, whose pace up front provided much-needed support for Suarez and introduced a different dynamic for the United defence.
Wisdom had the chance to make a name for himself having charged forward 70 yards to exchange passes with Suarez only to fire hopelessly wide.
Recovery: Steven Gerrard had to make a last-ditch challenge on Van Persie after giving the ball away
At that stage it appeared the game was up for the visitors but their first shot on target brought some hope.
A low strike from Gerrard, on a rare foray to United penalty area, was only parried by David de Gea and Sturridge used his poacher's instinct to follow up the rebound.
Audacious: Van Persie almost put United 2-0 up with this cheeky flick
Ok? Pepe Reina was helped by Martin Skrtel after running into Shinji Kagawa
Sturridge had the chance to snatch an equaliser and the headlines with five minutes to go after Suarez's determination saw the ball break to his strike partner but the £12million signing leant back and his effort sailed over and United escaped to consolidate their position as Premier League leaders
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