Is it possible to publish a simple result that refutes prior work in a leading journal? (without support from your advisor) In a certain field of science, it has been known that X leads to Y and assumed that if Y is observed it is caused by X. Using a relatively simple (mathematical) experiment, I have shown that also A, B, C, ... (class of certain objects), lead to Y, which means that observing Y does not guarantee X.

In my opinion, this is something that should have been checked years ago. In fact, this finding can be used to refute or at least considerably weaken the work done in a certain sub-field over more than 10 years. (though there's some prior critical work on this but the people do not seem to have cared)

Is it usually possible to publish such findings in leading journals? 

Another problem that I have is that the work challenges a major part of my supervisor's work, which rests on the mentioned assumption. She seems quite upset, and tries to see the work just as some technical quirk, which it is not. I joined the lab quite recently, so I have no idea what to do. Anyway, I am very serios about this: I'll resign if it necessary to get thing published as soon as possible. It could even end my career altogether but if science is not about truth I don't see why I would like to stay in it.

I am very early in my career and the most technical (mathematical) person in the lab. What I have shown is kind of similar as finding a counter-example in math.
The answer is yes.

But you paper will have to meet the standards of the journals you're aiming at (that might include experimental data) and show a good understanding of the existing body of work. Especially if as you state your work contradicts a lot of the existing literature, the level of scrutiny will be high. 

Now since you say you are quite early in your career it's possible that you are missing some aspects and that your work is not that controversial or that it is indeed just a technical quirk. In that case insisting in publishing it while ignoring your advisor's criticism will of course deteriorate your relationship and will probably mean you'all have to fined someone else to supervise you. But having it rejected will not affect your career negatively. Everyone gets paper rejected. Just make sure you don't make a habit of submitting work that claims to revolutionize the field but turn out to be wrong.


  I am [...] the most technical (mathematical) person in the lab


That might be true but it's very unlikely that everyone else in the field lacks the necessary mathematical skills to understand the issue.