There are times when a solution that was "googled" is beyond a shadow of a doubt the far superior approach to a problem or falls under best or at least better practices.
If this is such a case and you find yourself at a stalemate with your coworker about this, then it's important to go up the food chain and try to gently force the issue. Make your argument to your lead and present it in a respectful manner both towards him and in regard to your coworker, but be adamant about where you believe your approach is better.
Do your homework beforehand so you have a strong case: find out why your coworker believes his solution is better and listen. Then have a one on one meeting with your lead and present the issue. Present it from a technical standpoint, not as if it's a personal issue you're trying to resolve. It's not a race between you and your coworkers. It's most certainly never personal, then your well-researched case loses credibility. Be prepared to have your idea or standpoint shot down either way, that's the way it sometimes goes. Go there to talk but first and foremost, once you've made your case, listen to his or her why's and hows.
In the end, in many work environments (whether they be technical or not), due to either technical, historical or personal reasons, solution approaches might be chosen that are not always what google might tell you to be the ideal one or what you might think, are. We all know that.
Whether google is right (or whether you are) might in the end be of lesser consequence than deciding on a single approach that will be the standard to work by and that sort of team/technical decision is what your lead or manager is there for and can help achieve not only for you but for the whole team.
There is always deviation from a chosen standard or a chosen way of doing things -much to anyone's frustration from time to time-, but I personally feel it is very important to keep it at a minimum. It makes working with coworkers easier and it makes your work easier.