Thoreau's practice of non-violent non-cooperation is a fundamental example of the power of those who, apparently, are powerless according to societal structures. As Gandhi and Dr. Martin Luther King demonstrated, those who are oppressed are as necessary to the smooth working of an unjust social system as are those who rule such a system. When the victims of such a system refuse to cooperate, they cease being victims and actually are in control--those with political power or privilege must react or respond to those who refuse to cooperate with the system.
So, those who refuse to pay a tax, those who boycott businesses, those who peacefully disobey put those who are the source of the injustice being protested into a defensive or reactive stance. There is no basis for a violent reaction or response from those who have the political positions of power since the protesters have the practical power at that point.
Violence on the part of protesters justifies the use of violence from those in political positions of power. Political privilege abused constitutes a loss of that privilege as Jefferson noted in the "Declaration of Independence." True, non-violent power rests in the hands of those who refuse to cooperate with an unjust system or to obey an unjust law.
People often say that Thoreau's ideas helped to inspire people like Mahatma Gandhi and Martin Luther King, Jr. Thoreau was the first to lay out the idea that those two great men put into practice. This was the idea of nonviolent civil disobedience.
Thoreau believed that violence was wrong and that violence could not bring about justice. He believed that people who wanted to change unjust laws had to do so nonviolently. He also believed they needed to be willing to pay for their beliefs. So Thoreau believed that the way to fight injustice was to disobey the unjust laws and to accept the punishment for doing so.