I've had a similar issue. Take it to your team leader, it will probably be the fastest way of resolving things. Note that this is not you throwing your colleague under the bus, it is you trying to help him and the whole team be more efficient.
It is very important that your are transparent with your team. You are not trying to outsmart anyone or prove yourself, solving this issue is in the best interest for everyone on the team. Doing something like this without anyone knowing will only make them lose their trust in you.
He is a very skilled and very knowledgeable developer and most of the time his stubbornness is "healthy" for the team as he ensures we follow best practices and conventions, however, some times he is wrong and it is extremely difficult for him to admit it.
This is your subjective opinion. You are deciding he is wrong on some criteria you have. With most good managers/team leads a subjective argument won't fly well but good documented data will.
Start documenting the effects of this behavior and present the data to your team lead.
Depending on the type of project you are working on, when it comes to your opinion vs your colleagues', you both weigh in the pros and the cons of each approach and present it to the team lead. He can then decide what the best move is. Simply arguing between yourselves will solve nothing and will probably annoy your other teammates.