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.
Innocent Emeghara had a great chance to put Switzerland back on level terms after 52 minutes but he scuffed his shot straight at De Gea.
Switzerland upped the tempo and went close on several occasions from set pieces with Timm Klose and Pajtim Kasami heading wide from promising positions.
As the Swiss tired of chasing possession, Thiago put the result beyond doubt with a free-kick in the 81st minute.
Spotting Sommer off his line, the Barcelona midfielder floated the ball over his head from 40 metres out, triggering wild celebrations from the Spanish.
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.
