What turning points in history occurred from antiquity to the Industrial Age?
There are so many turning points that have occurred in history between antiquity (no matter how you define that) and the industrial age. I will mention two.
First, you have the rise of Christianity. The development of this religion changed the course of the history of Europe (and, by extension, of places that Europeans colonized). It created a new set of morals and ethics and helped to create a sense of pan-European identity.
Second, there is the rise of Islam. This did for much of the rest of the world (Africa and Asia in particular) what Christianity did for Europe -- it created a new set of ethics and a sense of common identity for all Muslims).
The rise of these two faiths helped to create our whole concepts of Europe and the Middle East. They continue to impact our lives today.