This is a huge question, and unfortunately one that has attracted lots of badhistory. It would help if you define your terms a bit. What do you mean by "dominance"? Military dominance? The West really only pulled decisively ahead militarily in last 150-200 years. That military dominance was definitely a unique moment, that has mostly evaporated. Military might has more to do with wealth and relevant investment than geographic location these days.

Do you mean the way Europe economically and politically dominated the Americas and then slowly Asia and Africa as well? The global nature of that was certainly unique. No imperial system extended to the whole globe before that.

A book for generally examining the question of when and why "Western" development passed "Eastern" development is Dr. Ian Morris's Why the West Rules For Now. It is, as he admits, chainsaw art. He defines the West as an civilization descended from the Mesopatamian advent of agriculture while the East he connects to the Yellow and Yangtze Rivers. He roughly measures their development right back from human migration out of Africa to the modern day. According to him, the West led until around the 6th century. The East then led until the 18th century. But the end of the book is spent discussing how everything since the Industrial Revolution is so different and will only become moreso. He suggests that the East may pass the West again this century, but we really have no idea what that will mean. Any more than William the Conqueror would understand spaceflight or the internet. The very nature of development is changing.