I think the Trans-Siberian rail still runs from Moscow to Beijing (with a link to the Trans-Mongolian rail at Ulan Ude or the Trans-Manchurian at Chita). From

I think the Trans-Siberian rail still runs from Moscow to Beijing (with a link to the Trans-Mongolian rail at Ulan Ude or the Trans-Manchurian at Chita). From Beijing it shouldn’t be too difficult to find a single link to Hanoi. And from Hanoi there is a single sleeper that runs to Ho Chi Minh (I’ve taken this one in the other direction back in 2008). So if I’m not mistaken (or out of date) Moscow to Ho Chi Minh should be at most 3 connections (Ulan Ude/Chita, Beijing, and Hanoi).