I'm also sure that most of us have come across that 'one piece of work of a slimeball'.
So how do/did you deal with that one office politician that one time?
If dealing with peer or higher-level "politicians" - I refuse to play their game, even if beneficiary to me at the time. While I simultaneously point out any transgressions of theirs. Sooner than later they screw up - since focusing on politics instead of your work is actually pretty hard work.
If dealing with subordinates. I perform "face thy accusor" ritual. It also helps not to get engaged into any of their schemes - thus preserving one's integrity.
Oh and both approaches require that you be valuable to the team - else you will get ground and ejected :)
And there are zillions of well sourced accounts where the key technical people at companies big and not so big lost political battles and then their jobs or ability to accomplish anything and the company then suffering or worse.
A lot of this comes down to Pournelle's Iron Law of Bureaucracy:
"In any bureaucracy, the people devoted to the benefit of the bureaucracy itself always get in control and those dedicated to the goals the bureaucracy is supposed to accomplish have less and less influence, and sometimes are eliminated entirely."
I'm really bad at even detecting these games until it's too late, and of course it's hard for anyone who's focused on the goals of the company to fight those who are focused on their position within it.
At the end of the day, other people in your office will see them for what they really are and appreciate your candor.
If you're ABOVE said politician, it's as simple as either bringing them into your office for a few private chats and explaining that you know what they're doing and you see through it... then letting them go if they don't fix it.
No factor has more impact on the outcome of software projects than politics.
I'd just treat everybody the same.
If anything, if you have a good "schmoozer" put him in a PM role or something. Use those skills to help the team perform better (if this is a possibility). If you can't do that, and you have some sort of antagonistic relationship with the office politician? If you're a blunt person like me, the best thing to do is to steer clear. People with highly developed social skills can be very dangerous to deal with unless your skills are close to the same level.