Spain took the lead within two minutes of the restart through Nico Williams. England came from behind, as substitute Cole Palmer drove in the equaliser on 73 minutes.
But their resurgence in the game was cut short as Oyarzabal, the Real Sociedad forward, turned in a cross in the 86th minute to hand Spain a record fourth European Championship crown, and a third in the last five editions.
They previously won in 1964, 2008 and 2012, the last two titles coming either side of their triumph at the 2010 World Cup during the golden era of Xavi Hernandez, Xabi Alonso and Andres Iniesta.
Spain have been comfortably the best team over the last month in Germany. England had hoped to finally claim a first men's international title since their fabled victory at the 1966 World Cup, but fell just short in their first ever final on foreign soil.