In the Battle of the Masts, in 655, the fleet of the Arab Caliphate defeated the numerically superior fleet of the Eastern Roman Empire off the shores of Anatolia.

I guess the Caliphate could be called an Asian power, though, at this time, they had conquered Egypt (which, of course is in Africa, and which was the source of many of their ships). Whether the Eastern Roman Empire could be called a 'European power' is also dubious. They held possessions in Asia and Africa, as well as Europe.

http://byzantinemilitary.blogspot.com/2011/09/battle-of-masts-655-ad.html

No, there were several, but possibly minor and insignifciant, victories of "Asian" countries in 16th century, just as the Portuguese started arriving.

First is the battle of Chaul in 1508, where Egyptian Mamluk fleet defeated the small Portuguese squadron. This "victory" resulted with one Portuguese ship sank, and death of the Portuguese squadron commander Lourenço de Almeida. The consequences of the battle was actually bad for Mamluk, as Lourenço was the son of the then-viceroy of India, Francisco de Almeida. Enraged and in seek of vengeance, the viceroy attacked and destroyed the Mamluk fleet in a decisive battle of Diu

Mamluks are technically Egyptian/African/Middle Eastern, but were in alliance with Indian Zamorin of Calicut.

If that isn't good enough, then there was the Battle of Xicaowanin 1522, where the Ming Chinese defeated a Portuguese fleet. The cause of the battle was Portuguese capture of Malacca ( a Chinese ally ) and general behavior of Portuguese appearing in the area.
Outcome was one Portuguese ship blown up, and one captured, from which the Chinese reversed engineered breech-loading cannons, which they promptly started mass-producing.

Do you consider the Ottoman Empire to be Asian?