How come the wings bank when I use the rudder

On a 3 hour cross country today I was amusing myself by flying with
rudder pedals only (all right, OK, a little yoke usage to maintain
altitude). But then I got to wondering why applying rudder pressure
causes the plane to bank. All I could think of was that rudder usage
produces asymmetric lift because one wing is somewhat blanked by the
sideways motion induced by the rudder? Also, the rudder surface is
above the plane's center of lift but I don't know how much of a factor
that is.