Ajax loading

I want to config my site so that links use AJAX to refresh specific divs without reloading the whole page (so that an embedded music player can continue to play without interruption).

I can do this just fine in non-WP sites, by using specific hard-code, but when using various plugins to do similar in WP the whole page reloads (I’m using a default TwentyFifteen theme as a test).

As these plugins offer various options I don’t need, I’m trying to find a way to add the non-WP code which I know works to WP and thus achieve my objective.