To ask for a PostDoc position in the university X, is better to do it by myself or to ask to my supervisor? I am a PhD student in artificial intelligence from an European university. This year I am going to finish my PhD program, so I am looking around to search for a suitable Postdoc position. 

I would like to apply to an important American university, named X.
In my research group here I have important professors that follow my work. One is my supervisor, an expert of artificial intellingence, and follows my work. The other is an expert of operating systems (i.e. different field from artificial intelligence).

This operating system professor in the 90s spent some years working at the preminent university X, and he still has a lot of contact and collaborations in that field.

Should I take advantage of this and ask him to contact my potential Postdoc advisor at the university to which I want to apply, even if he is from a different field?
Would it be worth?

His mail would be something like "Some decades ago I worked at your university in the operating systems field, and now I would like to recommed this candidate from artificial intelligence..."
Would this have sense?
Would this be useful?

Or would it be better that I contacted personally by myself this professor for the Postdoc position?
Put yourself in the shoes of the professor: what would they like best in a candidate? Contacting them yourself demonstrates more commitment than having your advisor do it for you. There may be cases where an introduction by a third party is best, but it seems to me it's better to use that only if really needed: guy is a superstar, your introductee knows him very well, or you are just trying to strategically probe whether a candidature would be well-received without actually getting involved yourself.

Also, you can get your advisor to follow up if you don't receive an answer, or just to help you when/if they are contacted as a reference.