Speaking in the US, the former Nato Secretary General and UK Defence Secretary urged Scots to "properly and soberly examine the impact of their decision" and said a "debilitating divorce" after a Yes vote would threaten the stability of the world.
In a speech at the Brookings Institute think tank in Washington DC, Lord Robertson said: "The loudest cheers for the break-up of Britain would be from our adversaries and from our enemies. For the second military power in the West to shatter this year would be cataclysmic in geopolitical terms.
"If the United Kingdom was to face a split at this of all times and find itself embroiled for several years in a torrid, complex, difficult and debilitating divorce, it would rob the West of a serious partner just when solidity and cool nerves are going to be vital.
"Nobody should underestimate the effect all of that would have on existing global balances, and the forces of darkness would simply love it."
Last night, one Coalition insider said Lord Robertson's language was "hardly helpful" to the UK Government's attempt to accentuate the positive pro-Union case, while a Labour MP described the remarks as "over the top".
For the SNP Government, Nicola Sturgeon expressed shock at Lord Robertson's "insulting and offensive" comments, saying his language did a disservice to the debate about Scotland's future.
Blair Jenkins, leader of Yes Scotland, emphasised how during the extensive debate on independence no-one had presented the prospect of a Yes vote in such "apocalyptic and menacing terms".
He said: "George needs to calm down and tone down the rhetoric if he wishes to make a meaningful contribution to what is a generally measured and even-tempered debate on the right democratic choice for the people of Scotland."
The Labour peer stood by his sentiments and stressed how he wanted other countries to speak out about the impact Scotland leaving the UK could have.
Meanwhile, in a speech in New York, Alex Salmond said an independent Scotland would be a "constructive" partner in Nato.
The First Minister said: "We won't have nuclear weapons; nobody seriously believes that a nation of five million people should be a nuclear-armed power. We will co-operate fully and constructively with our neighbours and partners, like the 25 Nato members, out of 28 which are not nuclear powers."
In a separate development, Alistair Darling, leader of the Better Together campaign, also in the US, stressed in a speech that Scotland could have the best of both worlds: enjoying its own identity, culture and heritage while being part of a strong United Kingdom. He said: "Being part of the UK doesn't mean we need to give up what is best about Scotland.
We can be fiercely proud of all that Scotland has achieved, without giving up the security that comes from being part of something bigger."
Mr Darling, taking part in an International Monetary Fund seminar in Washington on the recovery from the global financial crisis, said: "I know from my own time as Chancellor that being part of something bigger means greater economic security for Scotland."
He added: "The ability to pool and share our resources, rather than the burden falling on Scottish shoulders alone, is a clear positive benefit of being part of the UK."