United’s prolific Dutchman gave the Red Devils a 19th-minute lead when he outfoxed Daniel Agger, with his low finish skidding under Liverpool goalkeeper Pepe Reina.
Vidic extended the home side’s lead early in the second half after the Serbian defender inadvertently glanced Patrice Evra’s header into the Liverpool net from a Van Persie set-piece.
The visitors were much-improved in the final 30 minutes as Daniel Sturridge’s introduction caused United’s defence problems, with the England international scoring from close range to ensure a nervy final period for the Red Devils.
“It obviously doesn’t matter when you play Liverpool, it is a big game and I hope it’s an important result,” Ferguson told BBC Sport.
“We were fantastic until their goal, which inspired them. They made a fist of it in last half hour and it made it an engrossing game.
“We played well. It was as good a performance as we’ve produced for a while. When you play Liverpool you have to be at your best form to win and we were.”
United’s man-of-the-match Danny Welbeck heaped praise on his strike partner Van Persie after the Netherlands international scored his 17th Premier League goal of the campaign.
“Robin van Persie is different class,” said Welbeck.
“He produces moments in the game others can’t do and we are glad he is on our side. We had our gameplan and it worked really well in the first half.
“They came into it more in the second half but we got the three points and showed our character.”
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