Is it possible to publish a simple result that refutes prior work in a leading journal? (without support from your advisor)
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.