It is a known fact that Mahatma Gandhi launched a non-violent movement which freed the Indian subcontinent from the British rule on 15th August 1947. But was this the first instance that a freedom movement or a revolutionary protest succeeded by adopting non-violence? Had it been attempted anywhere before? If so, was it successful?
Probably the more appropriate answer is strike actions in general, as also Gandhi did a long hunger strikes himself. Labour strikes date back at least to the strikes of Deir el-Medina:
I am not sure that it is the first case, but an ancient example is the Boston Tea Party protest:
It followed with 8 long years of war and ended with the declaration of independence of the USA.
But I am almost sure that it is possible to find more ancient examples.
As nonviolence of the Tea Party has been challanged, I am adding another answer.
In Johannebourg, South Africa, September 11, 1908 Gandhi lead a non-violent protest of indians against Asiatic Registration Act.
Going out on a limb here, and feel free to disagree, but what about the growth of the early Church?
The growth of the Church in early centuries was a form of independence movement, inasmuch as early Christians simply wanted to practice their faith without fear of persecution. Also, the growth of the church (emphasis on the small "c"), meaning the local communities, is by its very nature non-violent. One could make a very strong case that the activities of the Church (the Vatican) does not fit in that category because of the Crusades, among other reasons, but I'd say that the church as a community of believers is rather closely aligned with a non-violent independence movement.
Again, just a thought.
How about Canada? Now, it wasn't exactly an independence movement, but here goes.
After the American War of Independence Britain's empire was diminished substantially, leaving Canada as England's chief North American possession. Yet, there were still many French settlers in Canada, and they did not get along very well with the British. In 1791, British prime minister William Pitt the Younger divided Canada into two sections (the British section and the French section) to ease tensions. But by the 1830s, Canada was again in turmoil.
Queen Victoria sent Lord Durham to investigate conditions in The Canadas, and he made these suggestions:
His plan was gradually enacted, and in 1867, the British North America Act made Canada a self-governing commonwealth.