First, the most reliable solution is to save the page manually, yourself, to a local hard drive of your preference, provided you keep good file hygiene and backups and so on. If there are multiple-page articles, you have to save each page of the article, though. You also can run into some issues with the more "interactive" websites and articles, particularly if they use flash or java apps (which means the html you save will only contain a link to some flash or java file elsewhere on their server, which means you're back to square one). You can also get all kinds of gibberish from broken links anyway if the pictures suffer link rot or the page refers to an external style sheet or any other of some large number of possible other problems.

I think the only way to avoid this in an efficient, one-click manner is to use a pre-processor that detects the relevant content and saves only that for you. I use Readability to do this for slightly different goals and purposes.

Pocket is a more popular choice usually, but I've had many negative experiences with it not syncing to the android app, not working well with certain browsers, not processing articles properly, not processing the whole article, or sometimes not processing articles at all and keeping only the link (which helps you diddly-squat since that's the whole problem you're having).

Fair warning: Readability does a complete pre-processing of the article for, well, readability. It will remove ads, sidebars, top-bars, often comments to articles, and once in a while it'll remove too much. It usually successfully detects multiple-page articles, but not always.