Single article separated into multiple pages makes Facebook Like button detect as completely separated articles

You can explicitly set the ‘like’ URL. If you play with the form FaceBook provides you can see how that works.

<div class="fb-like" data-href="http://example.com" data-send="true" data-width="450" data-show-faces="true"></div>

If you don’t set the URL the default is the current URL, so you will have multiple pages.

So, and this is the only WordPress part of this question, use the_permalink in that form.

<div class="fb-like" data-href="https://wordpress.stackexchange.com/questions/73447/<?php the_permalink() ?>" data-send="true" data-width="450" data-show-faces="true"></div>