Damn you, you snaked my fifth! 
Now it is back to the drawing board.
Okay, a bit obscure…
Battle of Cape Bon ( 468 ) - Vandals destroy combined Roman fleet, nail in the coffin for the Western Empire.
I would say yes…lets not limit it…any battle primarily based in water.
They should never have gone up against Sicilians when death is on the line! HAhahahahaha – *
In fact, the Athenians got the best of both worlds by starting a land war in Sicily.
As a newbie, wondering if there’s a case for the Battle of the Nile as being strategically more important than Trafalgar (considering the effect on land combat, strategic alliances, etc.)? Didn’t it pretty much keep Napoleon from threatening any overseas British possessions and pretty much permanently turn over control of the Med to Britain?
And I’ll throw out the Battle of the Chesapeake, which trapped Cornwallis’ army and forced him to surrender, thereby ending the American Revolution in victory.
I want in on that. 
Battle of Manila Bay – Led to Dewey being given the unique (at least for USA) honor of Admiral of the Navy
Battle of the Coral Sea – Introduction of aircraft carriers facing each other
Battle of Yamen – Mongol-controlled Yuan Dynasty crushed Song Dynasty in China
Battle of Cartagena de Indias – British beaten by Spain in Colombia
Battle of Noryang – Japanese invasions of Korea repelled
I came here to nominate Diu, the Downs & Battle of Myeongnyang, but since they’ve already been taken, I’ll throw out:
Aegospotami - Lysander’s destruction of the Athenian navy finished the Athenian Empire.
Marmara (677) - Greek Fire stopped the Arabs outside Constantinople - and the Byzantines would roadblock Islam for another 700 years.
Quiberon Bay - the cherry on the Year of Victory, it secured control over the Atlantic for Britain and doomed French Canada.
The Yalu - Japan’s victory was the start of Japanese imperial expansion, and a death blow to the Qing Empire.
Getting the US into the war is what makes the action so important.
*H.L. Hunley *sinking the Housatonic.
The first submarine to sink an enemy vessel.
See post 11.
Whatever its consequences, it’s pretty tough to quibble with its decisiveness. I can’t think offhand of any more lopsided outcome in the age of fighting sail.
Not sure if it counts as a naval battle per say, but I would throw out the Kamakazi “devine winds” origin. From Wikipedia:
The Mongol invasions of Japan (元寇, Genkō?) of 1274 and 1281 were major military efforts undertaken by Kublai Khan to conquer the Japanese islands after the submission of Goryeo (Korea) to vassaldom. Despite their ultimate failure, the invasion attempts are of macrohistorical importance, because they set a limit on Mongol expansion, and rank as nation-defining events in Japanese history. The Japanese were successful, in part because the Mongols lost up to 75% of their troops and supplies both times on the ocean as a result of major storms.
bump
The Battle of the Falkland Islands in World War 1 seems pretty decisive. What little remained of von Spee’s squadron after the battle was pretty much ineffective, and the British lost 10 men and no ships to the Germans losing over 1800 men and 6 ships.
Battle of Flamborough Head – I have not yet begun to fight!
Sinking of the Lusitania – One sided, but helped doom the Germans in the big picture.
Operation Dynamo – Evacuation of Dunkirk allowed the Allies to live to fight another day
OK, this one’s kind of obscure:
The sinking of the INS Eilat, 1967 - the first battle in which a vessel was sunk using ship-to-ship guided missiles. In a way, it led to as big a paradigm shift as the ironclad or the aircraft carrier; we just haven’t had a big enough naval conflict yet to see its impact.
Also:
The Battle of Baltimore, AKA the attack on Fort McHenry - strictly based on an importance-to-casualties ratio, this is a clear winner.
Not to mention the anthem we got out of it!
Does an amphibious assault count as a naval battle?