Even in a large station, 20 minutes is plenty of time to change trains. Remember, there's no security check or other barriers; you just get off your first train, figure out which platform your second train is on, and go to it. I don't know Utrecht station, but in many of them, to change platforms you have to go down stairs, through a passage connecting all the platforms, then up stairs to your platform. There are usually video monitors on the platforms and in the passageways, showing departing trains. Make sure you are looking at a departures monitor and not an arrivals monitor (just like at an airport). When looking at a monitor, look for the departure time and train number, not just for "Maastricht" (in case Maastricht is not the last stop).
Do know when your train is arriving in Utrecht. About 5 minutes before, gather your belongings and move toward the exit; you'll see others doing the same. That way, you exit as soon as the train pulls in. If you wait until the train stops to gather your stuff, people will have started getting on while you're still trying to get off, which is like swimming upstream, and is very difficulty with bags.
And if you ever get lost or confused, don't hesitate to ask for help right away. While taking trains is daunting for many who live in North America, for Europeans it's as routine as driving to the mall.
Here's Rick's introductory video about riding the rails in Europe, with other tips: http://tinyurl.com/ac82c92