After opening the scoring in the second minute with a close-range strike, Van Persie received a raking pass from Wayne Rooney before firing first time past Brad Guzan. The 29-year-old completed his hat-trick with another finish inside the box 12 minutes before half time.
"It was goal of the century for me," Sir Alex told reporters.
"It was marvellous. The technique with his head down, over the ball and just perfect timing. It was a magnificent strike. He scored exactly the same goal against Arsenal. He is in his mature years and winning the league tonight meant a lot to him.
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Van Persie is now one goal clear of Liverpool's Luis Suarez in the race for the Premier League's Golden Boot, while Sir Alex has compared the striker's impact to Eric Cantona's time at Old Trafford.
"When you identify a great player coming to the end of his contract, you go for him no matter who," he added.
"In terms of impact he has made as big an impact as any player I can imagine. [Eric] Cantona was an incredible impact player, I've had some great strikers, maybe 10 great strikers.
"We had an expectation of him. He was sensational last year, but Arsene [Wenger] said he was better than I'd think after I'd done the deal, and he was right. He has never disappointed us.
"He has been unbelievable, his early form was fantastic. He had a dry spell, as most strikers do, but he has come back from that and he was unbelievable tonight."