In v10.1 under Windows x64 I experience no "z-fighting" in this example when using the `"BSPTree"` rendering method.  This method may be individually using [`BaseStyle`](http://reference.wolfram.com/language/ref/BaseStyle.html)

    data = {{1, 1, 1, 1}, {1, 0, 3, 1}, {2, 0, 0, 1}};
    plot = ListPlot3D[data, Mesh -> None, InterpolationOrder -> 0, Filling -> Bottom, 
      FillingStyle -> {Opacity[1]}, ColorFunction -> "SolarColors", 
      ViewPoint -> {Pi, Pi, 5}]

    Show[plot,
     BaseStyle -> 
      RenderingOptions ->
       {"Graphics3DRenderingEngine" -> "BSPTree"}]

The same Option may be given in `ListPlot3D` but I separated it with `Show` for clarity.

It may also be set globally for a session with:

    SetOptions[$FrontEndSession, 
      RenderingOptions -> {"Graphics3DRenderingEngine" -> "BSPTree"}]

Or persistently by changing `$FrontEndSession` to `$FrontEnd` in the code above.

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Other cases where the rendering method is important:

- http://mathematica.stackexchange.com/q/15735/121
- http://mathematica.stackexchange.com/q/65260/121
- http://mathematica.stackexchange.com/q/88520/121

And one I just found which basically duplicates this question:

- http://mathematica.stackexchange.com/q/111945/121