The Dutchman came off the bench to net a sublime equaliser in stoppage time against West Ham as United salvaged a 2-2 draw from a thrilling FA Cup third-round tie at Upton Park.
It was Van Persie's 20th goal since joining from Arsenal in a £24million summer deal, converting a fine crossfield pass from fellow substitute Ryan Giggs after ghosting into the right side of the West Ham penalty area to force a replay.
Serbian defender Vidic hopes Van Persie can maintain his high standards over the course of the campaign as United chase another Barclays Premier League title and European glory.
"His touch is magnificent and his finishing is top class," Vidic said on MUTV.
"It is movement from the book, touch from the book, goal from the book.
"It is something they can show to kids, how to move and finish in the last third. He was magnificent for us, we just hope he is going to be in the same form in the end."
While quick to also praise "world-class" Van Persie, United manager Sir Alex Ferguson was left less than impressed by his side's defending at Upton Park.
After Tom Cleverly had swept the visitors into a lead midway through the first half, the Irons soon hit back when James Collins headed in a brilliant cross from Joe Cole, making a second debut after returning to boyhood club in a free transfer move from Liverpool.
West Ham then turned the tie around on the hour when Cole again provided the ammunition for Collins to leap above the static United defence and power a header past David De Gea.
Despite being rescued by Van Persie's moment of inspiration, Vidic accepts the team must tighten up at the back.
"We always know that on set-pieces they are a tough team to play against and eventually they scored two against us from crosses," the centre-back said.
"They scored from the second ball which we should look at again, and we are definitely a bit disappointed. It is something to talk about.
"We have the height in the team, we should deal better with that, but most important is that we managed to stay in the game."
Vidic maintained despite bigger prizes on offer for United this season, the FA Cup remains an important target.
"We did not win the trophy for the last eight years and it's a trophy we are looking to win," he said.
"We showed [that] in how we celebrated the goal, and I am hoping at home it will be a different game."
United's replay with the Hammers will take place on January 16, just after the home Premier League game with Liverpool and ahead of a testing trip to Tottenham.
Ferguson hopes his injury list will have eased somewhat to give him the opportunity to rotate once again in the middle of a tough run.
"I have got a good strong squad and I am sure players will all be back by the time we play all these games," the United boss said.
"Nani has started training as is almost fit now, Phil Jones should be ready in the next week or so.
"We have a strong squad, so why don't we use it?"
West Ham manager Sam Allardyce, meanwhile, admitted it was a "sickener" for his side not to have held on for what would have been a memorable cup scalp.
"It was a great performance from the lads and it is a real shame they didn't get us through at the first time of asking," he said.
"But we are still in the draw after a fantastic performance on the back of a very good [league] win over Norwich.
"I hope our bad run is now over and, if we continue to keep performances like this going, we will continue to get results."
Brazilian side Cruzeiro claim forward Wellington Paulista will join West Ham on a loan deal, which would further bolster Allardyce's attacking options following the move for Marouane Chamakh on a six-month contract from Arsenal.
"We are searching for players, but at this time of year an agent will ring me up, or he will contact the chairman and the next minute they ring the papers and say we are going to buy someone," said Allardyce.
"That happens throughout the window so until we have got one having a medical or nearly clinched then we will be linked with another 150 players between now and January 31."