Van Persie grabbed the first and third goals as United gave David Moyes a perfect Premier League debut with the club by hammering last season's Capital One Cup winners 4-1 at the Liberty Stadium.
The former Arsenal forward's goals came from two very different but equally brilliant pieces of finishing.
The first saw the 30-year-old show great agility to hook home a high bouncing ball, while a sublime left-footed strike ensured Michel Vorm got nowhere near the second.
Michu has been lauded as one of the top-flight's best finishers after scoring 18 league goals during his first season with Swansea, but he believes Van Persie, who scored 26 league goals last term, is in a different class altogether.
He said: "He had two chances and he scored two goals but that is why Manchester United are fighting for the championship.
"For me, to be honest, he is the best striker in the world.
"He had no clear chances in this game and it is just incredible how he ended up with two goals. It stops with him, he is the best.
"I don't know how many goals he will score this season. A hundred, maybe a thousand! One thing is for sure, he is going to score a lot."
Vorm knows Van Persie better than most as the pair are part of the Dutch international squad, and the Swansea goalkeeper also heaped praise on his compatriot.
He said: "The problem with Robin is you never know where he is going to put the ball. He scored the first goal with an incredible volley with his right foot and then the second one was an amazing shot with his left foot. It is so hard even when you know him well you can't work him out. I think he is in the top five players in the world at the moment.
"Even though he is an opponent he is a joy to watch. He can only help to make you better because you have to be on the top of your game against him. Otherwise you can see what happens. It is a shame he doesn't play for us."
Swansea must now dust themselves down and prepare for the first leg of their Europa League play-off tie against Romanian side Petrolul Ploiesti on Thursday.
And Michu is backing the Swans to recover quickly.
He said: "Manchester United are a better side than us, they have a lot of very good players, a lot of top players.
"For us it is difficult to compete with teams like that but we will try.
"But we can be happy because we did play well in parts of that game. We have to be strong in the mind, we will be ready to fight again on Thursday."