Hi DeadPoetic,
Have you verified that your host is secure as fw116 mentioned above? He's already covered most of the other possibilities as well. At least 25% of the posts in this Security forum relate directly to your problem.
This isn't related to Google Analytics or Joomla, it's a security problem with your site, host, or passwords. Malware distributors have been doing this for years, not just the past few days. The only difference in the past few days is that they have been modifying/replacing google analytics javascript instead of inserting their own iframe in order to obfuscate what they are doing.
As long as you follow the recommendations on the
official security checklist and these
basic Joomla! security recommendations your site will be secure without the need for things like jsecure or joomsuite defender.