After a fiery yet goalless first half, Spains Dani Olmo latched onto an inch-perfect pass from Spanish wunderkind Lamine Yamal to give La Roja the lead on 51 minutes.
Niclas Fuellkrug struck the post with 14 minutes remaining but with the hosts staring at an early exit, Florian Wirtz slammed in a Joshua Kimmich knock-down in the 89th minute to take the game to extra time.
With a minute remaining in extra time and the game looking set for penalties, Olmo lofted a cross for Merino, who headed Spain into the semi-finals and on course for a record-breaking fourth Euros crown.
Germanys exit brings to an end the hosts hope of a summer fairytale Euros victory after a decade of poor performances at major tournaments, while also lowering the curtain on Toni Kroos stellar career.
The battle between the two most successful Euros nations, with three titles apiece, was billed as a final come early, with the in-form Spaniards against Nagelsmanns reborn hosts.
