I have lodged a complaint to Senior management, but I'm worried I won't be taken seriously.
This might be an issue. As a senior manager with little visibility into every-day things, I would see a well-liked subordinate and someone who has an axe to grind. I'm making a lot of assumptions here, but I think this is an angle that should be considered.
Your colleague is excellent at playing politics. Do you know why totalitarian regimes get a lot of bad press? Because they do impactful things in a very visible way. Lodging a formal complain is very visible and impactful, because it ensures that someone will look at it, someone will take some action, and someone will be seen as looking into it and taking action. It creates a paper trail. It becomes official.
Convincing a senior manager to reprimand a star employee because you don't like him is a tough sell. It's much easier for the manager to find a way to deal with it which doesn't require impactful action on his side. He might, for example, decide to "take it under advisement", which is management-speak for go F yourself.
So your colleague is excellent at playing politics, and you have decided to take him on on his own terms. Let me explain: This guy said something which impacts your promotion (and career). You have, in turn, decided to target him, instead of any of the factors that gave him a foothold to put in a bad word against you, assuming that he ever did.
I would instead focus on my own performance and my boss's expectations of me. I would also push for regular one-on-one chats with my boss to better influence him, preferably without focusing my ire on a star employee.
I can't be any more specific cause I don't know the details of your issue, but I will sum all this up as: Fight the battle you can win.