Spain, dominant at senior level where they are world and European champions, sealed their third continental under-21 title thanks to a first-half header from Herrera and an audacious free-kick from Alcantara in the 81st minute.
Switzerland, who had been seeking their first trophy, managed to shackle the Spaniards well in the opening half hour in Aarhus and could have gone ahead when Xherdan Shaqiri half-volleyed a shot that goalkeeper David de Gea had to punch away.
Instead, the Swiss defence was breached for the first time in the tournament as Didac Vila's pinpoint cross found Herrera arriving at pace, and the midfielder planted his header firmly past keeper Yann Sommer at the near post in the 41st minute.
Earlier in the day, Yegor Filipenko scored an 88th-minute goal as Belarus beat Czech Republic 1-0 in the third-place play-off and qualified for next year's Olympic Games.
