The primary goal of documentation is not to ensure perpetual access to a source but to verify the publication facts of the version you consulted. Thus it is acceptable to cite the original version with the defunct URL:

Bluestone, Gabrielle. “Three Jailed in Myanmar for Posting Image of a Buddha Wearing Headphones.” Gawker, 19 Mar. 2015,  gawker.com/three-jailed-in-myanmar-for-posting-image-of-a-buddha-w-1692317287.    

If you subsequently fact-check your work using an archiving website such as Wayback Machine, however, we recommend that you cite the new version of the page that you have consulted; be sure to include the name of the original site in your entry:

Bluestone, Gabrielle. “Three Jailed in Myanmar for Posting Image of a Buddha Wearing Headphones.” Gawker, 19 Mar. 2015. Wayback Machine, web.archive.org/web/20150319101001/http://gawker.com/three-jailed-in-myanmar-for-posting-image-of-a-buddha-w-1692317287.