For some reason only this worked for me today. All other variants ended up in bad json error from API.
Besides, yet another variant for creating required POST request with JSON payload.
request.post({_x000D_
uri: 'https://www.googleapis.com/urlshortener/v1/url',_x000D_
headers: {'Content-Type': 'application/json'},_x000D_
body: JSON.stringify({"longUrl": "http://www.google.com/"})_x000D_
});
_x000D_