Disaster averted

Keep in mind that "disaster" is a relative term in this situation. One empire's disaster is another's opportunity.
A few examples come to my mind:
The Sea Peoples' invasion of Egypt in the late 12th century BCE.
Salamis, 480 BCE.
Pharsalus for Caesar, 48 BCE. Same with most of his subsequent campaigns.
The Third Century Crisis of the Roman Empire.
The last war between the Byzantine and Sassanian Empires, which, despite setting the stage for the Muslim conquests, ended up confirming the longevity of the Byzantines, who thereafter managed to beat off a Muslim siege of their capital in 717.
The An Lushan Rebellion, among other revolts from the later Tang period in China, albeit their defeat only staved off the Tang's collapse.
The large-scale rebellions that started popping up all around the Abbasid Caliphate after the Anarchy of Samarra.
Practically every engagement of the First Crusade could have jeopardized the venture if it had gone the other way.
The Mongol invasions of Vietnam and Japan during the reign of Kublai.
Much of the history of the Habsburg Empire, ranging from the wars with the Ottomans to the wars with Napoleon to 1848.
Siam's wars against Burma. The latter came close to destroying the former in the 1760's had the Qing Chinese not inexplicably decided they wanted to conquer Burma.
The British invasion of Afghanistan, the First Boer War, the survival of the Ethiopian Empire...
The Battle of Tannenberg in 1914.
 
An obvious candidate is the Battle of the Catalaunian Fields in AD 451. Defeat of the Romans and their allies could have led to even greater and earlier collapse of the West Roman Empire than in fact occurred. And two 'events', the two great divine winds of history: the typhoon that destroyed the Mongol invasion fleet off Japan in 1281, and the storm that scattered the Spanish Armada in 1588.
 
What event, situation or battle was averted which could have lead to a catastrophe if it weren't?

Well, “catastrophe” depends upon a point of view because there are always to sides to consider.

Take, for example, a battle of Vorskla. In OTL defeat of Lithuanian-Poliis-TO force is considering catastrophic but, if you look from a different side, Vitold’s victory could be considering catastrophic for the Horde, making it a vassal of the Lithuanian state. It can also be considering potentially catastrophic for the future consolidation of Russia making Great Princedom of Moscow an official vassal of Lithuania. Probably it could be if not catastrophic then at least unpleasant for Poland because greatly strengthened Lithuania could break the existing union. So can we said that Yesugei averted a major catastrophe by beating Vitold or that if Vitold won the (different) catastrophe could be avoided?

Or we can take a non-event (you wisely allowed for such an option). In 1812 by not following the initial plan of campaign the Russians avoided destruction of their armies near the border and eventually won a war. From the Russian perspective, the catastrophe was averted and blahblahblah. From the French perspective, this was catastrophic. However, in a broad perspective with a benefit of a hindsight there can be obvious questions about the general long-term “benefits” even for Russia taking into an account the losses suffered from the campaigns of 1813-14 (which were fought mostly for somebody else’s interests), future problems caused by acquisition of Poland, increasingly reactionary reign of Alexander I, stagnant economy, etc. (including the “legend of invincibility” which ended with a catastrophic CW). Of course, there can be broader speculations about the broader positive/negative results of the averted French catastrophe in 1812: pluses/minuses of the “Napoleonic Europe” (minus Spain) comparing to a generally reactionary system established in OTL Congress of Vienna.
 
An obvious candidate is the Battle of the Catalaunian Fields in AD 451. Defeat of the Romans and their allies could have led to even greater and earlier collapse of the West Roman Empire than in fact occurred. And two 'events', the two great divine winds of history: the typhoon that destroyed the Mongol invasion fleet off Japan in 1281, and the storm that scattered the Spanish Armada in 1588.


Taking into an account that in OTL soon after his presumably catastrophic defeat Atilla invaded Italy and victorious Roman side could do nothing, I’d be rather skeptical about strategic results of that victory (later analogy - Battle at Kulikovo with almost the same follow-up scenario where the defeated side can launch an offensive shortly after defeat and a victor can’t repeal it).

As for the Mongolian invasion of Japan (percentage of the Mongols in each of these invasions is an open question, almost definitely well under 50%, most of the troops and all sailors being Chinese and Koreans), one of 1274 failed without any divine interference and there are opinions that size of the invading force of one of 1281 is grossly exaggerated, especially the Japanese assessment of the numbers), which makes a true importance of a typhoon rather questionable: even before it the invading force was defeated in the Second Battle of Hakata Bay and forced to reembark and after typhoon there were battles on various islands in the last of which the Mongolian army of allegedly 100,000 (Japanese numbers, seemingly typhoon did not cause too much of a destruction after all :) ) was annihilated. Tendency to exagerrate numbers is anything but unique and both ancient and medieval sources had been routinely doing this without any restraint.

Spanish Armada (the 1st one) was a part of an over complicated plan, which involved synchronization with an army sailing from Antwerp (using the boats which even its commander considered inadequate for the task) and the whole enterprise was heavily relying upon expectation (or rather a wishful thinking of the few English emigrees who managed to convince Phillip II) that the landed force would be supported by a national-wise Catholic uprising. What’s even worse for the whole national legend is the fact that the true military purpose was to stop the English help to the Dutch rebels and that, with the war in the Netherlands going on, Parma could not stay out of his main theater for any prolonged time (and neither did he had enough troops to conquer and held a country as big as England).
 
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