MySQL Connections slows down my website
You do not mention what language your application is in but if you are connecting on every page requested you could add a lot of speed simply by using a database connection pool. That way you application will not need so many connections and will not have to connect on every request, giving you extra speed simply because you don't reconnect every time and also reducing drastically the number of concurrent connections it uses, which seems to be your problem.

I have only seen problems like this you mention on Windows machines. Most of this problems are also highly attenuated simply by moving your db to GNU/Linux (or BSD).