Microsoft has released updated Web Tools 2013.1 that provide the support:
Note that I had to install it manually from the second link, the tools did not install properly from Web Platform Installer. Also a colleague had to install both Update 4 and these tools to get proper support.
Original answer (not actual anymore):
I received this answer from Microsoft developer:
MVC 5/Razor 3 tooling support for VS 2012 has not shipped yet. We hope to ship this support in Mid November.
Recently ASP.NET Program Manager from Microsoft mentioned in a talk that this would be included in VS2012 Update 4. Edit: unfortunately the support is not in Update 4.
So the accepted answer is true for now but we can plan to soon have this support in VS2012 as well.
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