The Battle of the Coral Sea.
http://en.wikipedia.org/wiki/Battle_of_the_Coral_Sea
The battle of the Coral Sea
The Battle of Savo Island.
I don't know about major, but the first naval battle in the historical record was Hittites defeat Cypriots near Cyprus
The Battle of Hampton Roads.
The Battle of the Coral Sea, history's first clash of aircraft carriers; the Battle of Midway, history's first DECISIVE clash of aircraft carriers.
Battle of Midway
The first naval battle in history between aircraft carriers was the battle of the Coral Sea in 1942.
Battle of Midway battle of Sicily
Largest naval battle in history.
Largest naval battle in history.
The Battle of Savo Island.
Battle of the Coral Sea
This was the Battle of Jutland
It was the first time in naval history that ironclad ships faced each other.
Leyte Gulf.
The Naval Battle at Penobscot.
The Battle of the Coral Sea was revolutionary. Coral Sea was the first naval clash of carriers, and the first naval battle in history in which all fighting (combat) was conducted by flying machines instead of warships.
The "Battle of the Coral Sea" was history's first sea battle between aircraft carriers (airplanes fighting the whole battle) in 1942. The "Battle of Tsushima" was history's first & only (last) decisive sea engagement fought between modern steel battleship fleets in 1905.