Adendum: Ok I realize that "global importance" isn't really the right term for this. What I am trying to ask is what was the role of europe in the grander scheme of pre-columbian Eurasia. Specifically what military, cultural, trade, etc influence did Europe as a whole have.
How are you defining "global importance" in a time when much of the world was not in regular contact with each other?
The "Age of Discovery" certainly brought Europe into the global arena.
The discovery of the Americas definitely added to the global reach and economic wealth and importance of Europe.
The other arc of European discovery in the age of discovery, around the Cape of Good Hope and into the Indian Ocean, was equally critical, however, in expanding the global importance of Europe.
In 1509, Portugal won the naval battle of Diu, which gained them control of the Indian Ocean against the Ottoman Empire, the Mamluks of Egypt, and various Arabian and Indian sultanates.
With this control, the Portuguese, established trade and bases that extended across the Indian Ocean and the Pacific all the way to Japan. They also undercut the old trade routes through the Ottoman Empire and Egypt, to gradually cut off valuable finances from their Muslim rivals and enrich Western Europe. (Of course, the Portuguese were later challenged and displaced from Indian Ocean dominance by the Dutch and the English).
This extension of power (enabled by the uniquely effective European cannon armed, strongly built, seagoing, ships) and commerce into the Indian Ocean was contemporaneous with the discovery of the Americas, but was equally important in extending the global power and influence of Europe.