Naval battles with the largest possible historical consequences

Which sea battle might create the largest historical changes if its outcome were reversed?

The Mongol invasion attempts against Japan and the Battle of Lepanto are strong candidates because their consequences reach far beyond naval tactics.

Two examples show how a reversed naval outcome could create changes far beyond losses at sea. The Mongol-led attempts to invade Japan are one possibility because success could transform the archipelago's later political development. Lepanto is another because it pitted the Holy League against the Ottoman Empire at a major Mediterranean turning point. The answer does not rank the examples conclusively, but it directs viewers toward naval events whose effects extend well beyond the immediate battle.