Watch the I Feel Ya online guitar lesson by Jeff McErlain from Soloing the Changes
What we have going on here is called modal interchange. The song changes keys actually, but it's easier to see it as changing modes although it is the same thing. The chord progression is D-F-C-D basically. Let's spell those out: D=DF#A, F= FAC, C= CEG. Already your Spidey senses should be tingling about that F# and F notes. One key cannot contain both, so we have changed keys.
We can also see it as changing modes from D Dorian (DEFGABC) to D Mixolydian (DEF#GABC). Pretty cool and pretty common, in the best way. It's a simple concept, but I know it's not that easy to think about modes and keys if it's new to you, so here's the trick... Just think about changing the one note you need to change, F to F#. There, you've changed modes.