To control Pandora, you should use a desktop application rather than the pandora.com website.
There are several options:
1. PandoraOne Desktop, which is Pandora's own application. It requires a subscription to the PandoraOne higher-quality, ad-free streaming service, which carries a yearly fee.
2. PandoraBoy, a free application which effectively wraps the pandora.com website and allows it to be controlled in various ways, including Rowmote.
3. PandoraJam, a $15 shareware application which adds a number of additional features to the basic Pandora package and allows Rowmote to control Pandora.
The features controllable by Rowmote are the same for any of the above options. Here are the button mappings on the Rowmote remote control:
Play: Play / Pause
Up: Volume Up
Down: Volume down
Left: Thumbs Down
Right: Next song
Menu: Thumbs up