One way is to upload the command line version of 7-Zip, it's a standalone .EXE file.
Next, from the Azure Portal, 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:
One advantage in using Kudu is that you can upload files directly in the browser just by drag&dropping them.
Hope it helped!