Unzip file uploaded to Azure Websites

This is possible using the Azure portal's console.

1. Navigate to portal.azure.com.
2. Locate your website (Browse->Websites, click on name of the website you uploaded your ZIP file too)
3. Scroll down until you see the "Console" button. By default, this is on the righthand side about three-quarters of the way to the bottom of the icon list (or "blade" in Azure portal parlance). The icon looks like this:

4. Navigate to the directory you uploaded your ZIP to using the cd command, just as you would on a typical console or shell window.

5. Execute unzip archive.zip where archive.zip is the name of your ZIP file.

Note that as of today, the unzip command will not output any progress reports; it runs silently. So, if you have a large archive that takes some time unzip, it may appear as if the command has hung, but in fact it is working and you just need to wait.
Update Sep 2018: The unzip command outputs its progress to the console, e.g.:

Archive:  archive.zip
   creating: archive/
  inflating: archive/203439A9-33EE-480B-9151-80E72F7F2148_PPM01.xml  
   creating: archive/bin/
  inflating: archive/bin/some.dll

One way is to upload the command line version of 7-Zip, it's a standalone .EXE file.

Next, from the Azure Preview Portal Azure portal (2014), navigate to your Website, click on the console tile and type the unzip command:

7za x thezipfile.zip

An alternative to the portal is to use the console from Kudu. Insert "SCM" between your Website name and azurewebsites.net like this to launch Kudu:

yoursitename.scm.azurewebsites.net

One advantage in using Kudu is that you can upload files directly in the browser just by drag&dropping them.

Pretty cool.