the standard awesome prompt just doesn't provide this function, you'd have to switch to a different one, I'm using http://code.google.com/p/bashrun2 which behaves very much like standard bash, it won't do the firefoxy thing though (unless you use things like !f[ENTER]). After installing bashrun you need to edit /etc/xdg/awesome/rc.lua to change mod+r default behaviour, find the lines:
-- Prompt
awful.key({ modkey }, "r", function () mypromptbox[mouse.screen]:run() end),
and by applying information from http://awesome.naquadah.org/wiki/FAQ#How_to_use_a_keycode_in_a_keybinding.3F we arrive at something like
-- Prompt
awful.key({ modkey }, "r", function () exec("bashrun2") end),
This seemes fine to me, but I havent tested this lua code myself.
Hope this helps.
EDIT:
I (the original poster) had to do:
awful.key({ modkey, }, "r", function () awful.util.spawn('bashrun2') end)