Battle of Midway.
I don't know about major, but the first naval battle in the historical record was Hittites defeat Cypriots near Cyprus
Battle of Midway
The Battle of Trafalgar.
The Romans (Duilius) inflicted a significant naval defeat upon Carthaginian (Hannibal Gisco [Not the famous Hannibal Barca] ) naval forces at the Battle of Mylae .
The Battle of Trafalgar.
Battle of Actium
Trafalgar, a battle he lost to the English due to his crossing of the T's (naval tactic) and their flag communication.
The Naval battle at Trafalgar.
The first naval battle in history between aircraft carriers was the battle of the Coral Sea in 1942.
The U.S. were stuck on a tiny island in the pacific ocean. Where japans' superior experience with naval ships had an advantage. But soon the U.S. took the offensive position.
The Battle of Midway ended because the naval forces of Japan withdrew from the battle. After losing four front-line carriers, and not meeting the objective of crushing the American naval forces, Japan's Navy retreated in defeat.
The naval, Battle of Midway, is considered to be the turning point in the American war with Japan. The defeat and destruction of the Japanese naval force, meant that Japan could no longer pose a significant naval threat at sea.