Reading your question, it seems to me that you re implying that the word needs to evoke the feeling of the person who has been brought down.
What about crush? It fits your main stipulation,
I'm looking for a word to describe rendering a person powerless
and can certainly include the elements of "power" and "group dynamics" in your example, albeit without specifically addressing them.
Here is the pertinent entry from Macmillan:
to completely defeat someone who is opposing you, especially by using force or violence Any anti-government protest was swiftly crushed.
To defeat someone in a game, competition or argument: defeat, win, beat... to easily defeat someone who is competing against you
While crush has emotional content, in the sense that the person in question might feel crushed, the word deflate hints at the idea of "puffed up" pride as well.
Applying it to the example in the question:
My expert destruction of his faulty logic left him completely deflated.
2 Make (someone) suddenly lose confidence or feel dispirited.
‘the news left him feeling utterly deflated’
to make someone feel less confident or important
Peter’s comments completely deflated the boy’s confidence.
to make someone feel less important or less confident
Otherwise, some phrases express your idea well:
I was able to put him in his place with my expert destruction of his faulty logic.
Oxford Online: put someone in his or her place
I was able to knock him down (quite) a few pegs with my expert destruction of his faulty logic.
Oxford Online: take someone down a peg or two
Both of these phrases manage to capture the ideas of crushing and humbling, showing that the person had been feeling superior to you.