V-2 is progenitor of all modern rockets, but it's difficult to call it "minimal modifications":
compare http://en.wikipedia.org/wiki/File:Fus%C3%A9e_V2.jpg ,http://en.wikipedia.org/wiki/File:V-2_rocket_diagram_%28with...
and http://en.wikipedia.org/wiki/File:R-7_%287A%29_misil.svg, http://en.wikipedia.org/wiki/File:Sputnik_8K71PS_grey.svg