Get a good teacher, it can really make a huge difference.
Practice difficult passages slowly (surprise!) and concentrate on relaxation. Often when I get tense, it's because I play faster than I think (like, my thoughts come after my hands). So, when you practice (slowly), try to think ahead, and when you speed up, try to keep it so that your thoughts are just a bit ahead of your hands. This helps in getting the movements more fluid. Also, think about groups of notes instead of single notes, otherwise you probably cannot do this very fast.
One trick which may help is to watch pianists with excellent, economic techniques (check for example Hamelin or Zimmerman on YouTube) play and try to imitate them; try to imagine how it feels when they play and then do it yourself with the piece you're practicing. You could also get a big mirror beside your piano so you can see what you're really doing when you play (posture, hand position, etc) and fix it immediately.
Anyway, getting a good teacher is the best thing you can do, really:
EDIT: A good teacher is indispensable because that way you'll get immediate and accurate feedback, and advice which best helps with your current problem. You say your wrists and whole body gets tense when you play. But what's the reason? Is it just bad posture? Is it because your hands move faster than your brain? Is it because you use too much force? Is it because you move too much or too little? Is it just because you're used to getting tense when doing difficult things? It's very difficult to figure the reason out yourself and even more difficult to try to fix it. That's why you should get a (good!) teacher, who knows all these possible reasons, can accurately detect what you do, knows what you should do, and is there to remind you until you learn it.