Geometric Topology is full of such examples. Perhaps the most dramatic of all were Milnor's construction of exotic 7-spheres and counterexample to the Hauptvermutung.

Since Poincaré, it had been widely believed that smooth manifolds and PL manifolds were two formalisms to describe one and the same class of objects, and proving that they were equivalent seemed almost like a fiddly technical detail. Indeed, in 3-dimensional topology (where the categories do happen to coincide, by work of Whitehead, Munkres, and others), people switch from smooth to PL objects and back ten times in the same paper, or even inside the same proof, without giving the matter a second thought. Statements like "corners can be smoothed" are mentioned with hardly a wave of the hand, almost derisively. So the fact that the categories don't coincide, and that the difference between them is meaningful and interesting, was a huge shock to topology, and has shaped a large part of the research in the subsequent half-century.

In an entirely different direction, Francisco Santos's Counterexample to the Hirsch Conjecture was a great surprise... the Polymath 3 Project originally had, I think, the dream-goal of proving it; and my understanding is that, since 1957, the vast majority of people had believed it to be true. The counterexample is interesting, and seems to be framing currect work on the Polynomial Hirsch Conjecture at Gil Kalai's blog.

Geometric Topology is full of such examples. Perhaps the most dramatic of all were Milnor's construction of exotic 7-spheres and counterexample to the Hauptvermutung.

Since Poincaré, it had been widely believed that smooth manifolds and PL manifolds were two formalisms to describe one and the same class of objects, and proving that they were equivalent seemed almost like a fiddly technical detail. Indeed, in 3-dimensional topology (where the categories do happen to coincide, by work of Whitehead, Munkres, and others), people switch from smooth to PL objects and back ten times in the same paper, or even inside the same proof, without giving the matter a second thought. Statements like "corners can be smoothed" are mentioned with hardly a wave of the hand, almost derisively. So the fact that the categories don't coincide, and that the difference between them is meaningful and interesting, was a huge shock to topology, and has shaped a large part of the research in the subsequent half-century.

In an entirely different direction, Francisco Santos's Counterexample to the Hirsch Conjecture was a great surprise... the Polymath 3 Project originally had, I think, the dream-goal of proving it; and my understanding is that, since 1957, the vast majority of people had believed it to be true. The counterexample is interesting, and seems to be framing current work on the Polynomial Hirsch Conjecture at Gil Kalai's blog.