The Welsh pass masters face the Premier League's joint top-scorer van Persie - alongside Swansea's Michu with 12 goals - at the Liberty Stadium on Sunday.
Williams said: "Van Persie's on fire at the minute and playing with a lot of confidence so we just have to work to stop him and stop the service into him.
"He's going to get a couple of chances, that's just the way it goes against a quality team, but I think we have to dominate possession and starve them.
"He's definitely one of the best strikers in the Premier League if not the best. He's a good player, technically he's very good and you can all see his goalscoring abilities.
"He's a complete player and was one of the best strikers I played against last season.
"You watch Manchester United so many times so you know what they're all about - trying to stop them is just a different thing."