The Spanish-American War was not a particularly advanced war in terms of its technology. There were no airplanes and no machine guns. It was not a war that was won or lost because of technology.
On the American side, there were only two weapons that can really be seen as technologically advanced in any way. The first of these was the Model 1896 Krag-Jorgenson Rifle. This rifle was advanced because of the fact that it used smokeless powder (new to the US) and because it had a five shot magazine instead of being a single shot rifle. Most American units, however, did not have this weapon because it was quite new. Second, the US used the 1895 model of the Gatling Gun. This was not a machine gun, but it was a weapon that could fire very rapidly. The rate of fire of this weapon was considerable and it did help the US win the war.