You can do this by using something called a Control Adapter.

Here are a couple of links to get you started

 - [Removing Web Parts tables in SharePoint][1]
 - [Remove Web Part Zone table with Control Adapter][2]

  [1]: http://blog.mastykarz.nl/removing-web-parts-tables-sharepoint-2010/
  [2]: https://sharepoint.stackexchange.com/questions/90030/add-css-class-to-webpart-cell