The latest version of VS Code installed a few days ago (the October 2017 update) keeps adding all kinds of strange import statements to the top of the .ts code file.
As of August 2018 (1.25), the accepted answer doesn't always work.
Instead, add this line to your folder-specific setting.
{ "typescript.preferences.importModuleSpecifier": "relative" }
Don't figure what's going on here, but those automatic path changes never happen in my environment.