Emotional manipulators drive you crazy because their behavior is so irrational. Make no mistake about it -- their behavior truly goes against reason, so why do you allow yourself to respond to them emotionally and get sucked into the mix?
The more irrational and off-base someone is, the easier it should be for you to remove yourself from their traps. Quit trying to beat them at their own game. Distance yourself from them emotionally, and approach your interactions with them like they're a science project (or you're their shrink if you prefer that analogy). You don't need to respond to the emotional chaos -- only the facts.
Maintaining an emotional distance requires awareness. You can't stop someone from pushing your buttons if you don't recognize when it's happening. Sometimes you'll find yourself in situations where you'll need to regroup and choose the best way forward. This is fine, and you shouldn't be afraid to buy yourself some time to do so.
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Most people feel as though because they work or live with someone, they have no way to control the chaos. This couldn't be further from the truth. Once you've identified a manipulator, you'll begin to find their behavior more predictable and easier to understand. This will equip you to think rationally about when and where you have to put up with them and when and where you don't. You can establish boundaries, but you'll have to do so consciously and proactively. If you let things happen naturally, you're bound to find yourself constantly embroiled in difficult conversations. If you set boundaries and decide when and where you'll engage a difficult person, you can control much of the chaos. The only trick is to stick to your guns and keep boundaries in place when the person tries to cross them, which they will.