If you click and start dragging the file and then press Command-~, the Finder will not rotate through windows. Instead, try this. Click and hold on the file you want to drag but do not start dragging. Now press Command-~ to rotate through the open windows, stopping when the window you want is frontmost. Now start dragging your icon, and drop it wherever you like in the chosen window.
Also, if you are dragging a Application from a downloaded disk image, you can click and hold on the icon and press Command-Shift-A (or any of the other shortcuts in the Go menu), and the Applications window will pop to the front -- then you can continue to drag your file into it.

