But the latest meeting between England’s two most successful clubs saw Liverpool ensured a nervous finish for United when substitute Daniel Sturridge pulled a goal back with just over half an hour left.
Victory saw United move 10 points in front of second placed Manchester City ahead of the champions match away to Arsenal later on Sunday.
Van Persie scored in a dominant first half for United with Vidic, deflecting in a header from Patrice Evra, adding a second goal in the 54th minute.
But three minutes later, Sturridge pulled a goal back for the visitors, who remained in eighth place but now trail United by the huge margin of 24 points.
Liverpool, in what is always one of the showpiece fixtures of the English season, looked unsettled from the off and fell behind to their north-west rivals in the 19th minute.
A well-worked move between Danny Welbeck and Tom Cleverley saw Evra clear down the left and he played in a low cross for van Persie, who calmly side-footed past Liverpool goalkeeper Pepe Reina to grab his 17th Premier League goal of the season.
It was certainly something for Jose Mourinho, the Real Madrid coach, to note as he was in attendance to cast his eye over United — the Spanish giants’ last-16 opponents in the Champions League.
Van Persie could have doubled United’s lead six minutes later but after Ashley Young found him free in the area, the ball bobbled before he could hit it and his strike flew harmlessly wide.
As Liverpool failed to create a single chance in the opening half hour, they were also gifting opportunities to United.
Joe Allen misplaced a pass near his own area that fell to Welbeck but Daniel Agger was on hand to make a last-ditch tackle and block the striker’s shot.
Allen was at fault again five minutes before the break when his tame header failed to clear the area. Cleverley caught it on the volley but his effort flew just inches past the post.
A superb ball from Michael Carrick then set Rafael da Silva away down the left and the Brazilian, despite losing his footing, got away from Glen Johnson before feeding van Persie.
However, the Dutchman’s clever flick was cleared off the line by Martin Skrtel.
Liverpool manager Brendan Rodgers had to do something at the break and he brought on recent signing Sturridge.
In the 51st minute, Liverpool squandered their best chance yet when Luis Suarez played a ball out to young defender Andre Wisdom but, caught in two minds as whether to cross or shoot, he sliced an effort well wide.
And they were punished as three minutes later as van Persie turned provider with a curling free-kick that found Evra unmarked at the back post and his headed went in off Vidic.
But Sturridge revived Liverpool in the 57th minute when David de Gea palmed Steven Gerrard’s shot into his path.
It was the striker’s second goal in as many games for Liverpool since joining from European champions Chelsea.
Reina then had to be alert to save Japan star Shinji Kagawa’s curling effort.
Then, in the dying moments, the ball fell to Sturridge following a period of sustained Liverpool pressure. But he curled his shot over the bar and United clung on to all three points.