The 70-year-old manager says the Dutch striker can prove to be the deciding factor in the title race, ahead of his side's top-of-the-table clash against league leaders Chelsea
Speaking ahead of his side's trip to Stamford Bridge to face Chelsea, he said the Dutch international striker is getting better by the game as he builds up his match fitness.
Signed for £24 million, the former Arsenal forward has already notched eight goals and three assists for United and the early signs of a deadly partnership with Wayne Rooney were clear to see in United's 4-2 win over Stoke last weekend.
“Robin’s performances are getting better all the time now,” Sir Alex told The Mirror. “He’s got there with his fitness, which is fine now.
"Last week against Stoke and on Tuesday against Braga, his movement was fantastic. I really was impressed with that.
"Robin’s cross last week [against Stoke] for Wayne’s goal was the kind of cross a defender hates - it was whipped in, between the last defender and the goalkeeper. It was brilliant.
“I thought it was really top, top stuff. Hopefully it does make a difference. We bought him for that reason - to make a difference.
“When we realised Robin wasn’t going to sign for Arsenal, we did our very very best to get him at our club and we succeeded.
“We’re delighted with that and the signs have been terrific. Robin is a great professional. He trains very well and he has made an impact immediately."
Van Persie's arrival seemed to spell the end for Javier Hernandez's first-team chances, but after his match-winning display against Braga, the manager feels there is a healthy sense of competition in attack.
“We bought him in to give us maturity up front, and also the flexibility of different types of players," Sir Alex explained.
“With Danny Welbeck, Chicharito, Van Persie and Wayne Rooney we have fantastic alternatives.
“The four of them could make the difference."