There are a few questions here, one of which I'm better equipped to answer than the others, so I'll do my best here and let my friends on the mod-team decide if this will work.

Did technological breakthroughs make his voyage possible, or was it a question of will?

I'm always a bit hesitant to use "technology" as a reason for something historical happening. Certainly, Columbus' ships were different from those that the Norse, who had previously landed in North America, were -- they were built differently (carvel- rather than clinker-built), had more masts and types of sails and could point up further into the wind, and were built deeper to carry more cargo than the Norse ships. Still, the Norse were reaching (northern) North America from Europe around the year 980 or so, and Columbus did not sail to the Caribbean until 1492. Columbus didn't "tech to caravel" and then gain the ability to enter ocean squares; at the same time, though, it's easier to work up against the wind and currents with a caravel than a longship with its square sail. That said, there's no particular technological reason the Norse couldn't have kept working their way down the coast from Newfoundland; it's more likely that tenuous links back "home" and lack of interest, as well as pressure from North American natives, played a role.

A "softer" technology, if you will, is his knowledge of how to use the prevailing winds and currents to make his voyage easier. From an older answer:

Columbus had some knowledge of the circular wind patters of the Atlantic, though it's not clear where he got those from.

In Columbus' time, Portuguese explorers had been using carracks and caravels to explore the African coast; those ship types were handier in sailing upwind than earlier types. But early exploration of Africa was limited by the stowage of ships, and how long they could remain at sea without re-provisioning; because sailing upwind took much longer than downwind, the return voyage was a constraint.

In Columbus' first voyage in 1492, he made it across the Atlantic to the Bahamas in about five weeks, following the prevailing westerly winds; he was able to return home by turning north and using the prevailing northeasterly winds and currents off the American coast, which turn east, to return to Europe by a more northerly route. The pattern of currents was known to Portuguese explorers, though the precise source of this is unclear.

Some historians have speculated for a number of years that the Portuguese, who were fishing on the Grand Banks for cod before Columbus' voyage, had established small camps in Nova Scotia or the region to dry cod -- I think Kurlansky talks about this in his pop history book Cod -- but in any case, they seem to have gotten there by following the prevailing winds to the southwest from Portugal, crossing the Atlantic partway and then catching the Gulf Stream to the Banks. (In sailing, the shortest distance is rarely a straight line.)

It's fairly clear, though, that what Columbus thought he was going to run into is Japan. He thought both that the earth's circumference was smaller than it is, and that Eurasia is wider than it is. Here's an older answer on that topic:

Columbus appears to have thought that the earth's cicrumfrence was about 25% smaller than it actually is. We know that he corresponded with Paolo dal Pozzo Toscanelli, a Florentine scholar who believed that sailing west would be a feasible way to reach Asia. Toscanelli had a map, possibly based on Martin Behaim's globe, that showed Asia extending much further east than it does, and the Azores, Canaries and Cape Verde islands extending much further west than they do (the Azores would end up right off the coast of Labrador in Behaim's projection).

Still, Toscanelli thought the Atlantic (from Asia to Europe) was about 5,000 miles wide; Columbus on the other hand interpreted Asia as being much bigger, thinking the Atlantic was only about 3,200 miles wide.

So, to sum up ... I don't know if I'd call his voyage a triumph of technology, or a triumph of the will, as much as a triumph of salesmanship, wishful thinking and dumb luck. Certainly when he got back to Europe, many other countries started being interested in voyages (assuming they could fund them, or have nobles fund them) -- John Cabot comes to mind, who explored North America for England. The Portuguese, who had interests in Africa and the Indian Ocean already by the time Columbus sailed, fairly quickly negotiated with Spain (well, Castile) to divide the globe in the Treaty of Tordesillas. (They had to sort out the other side of the world later, in a dispute over the Banda Islands in present-day Indonesia.) And, of course, "triumph" is a word I'm using here a bit sarcastically -- the devastation wrought by European colonization and genocide in the New World is not to be overlooked.