All eyes were on Julen Lopetegui's Madrid in the clash, as they took the field for the first time in a competitive game since losing Cristiano Ronaldo.
Lopetegui has thus far declined to replace the Portuguese with a new striker, but Costa's early exploits may just make him think twice.
Costa advanced up the right flank and smashed past Keylor Navas in the first minute of action in Tallinn, beating the goalkeeper from an acute angle at his near post.
It took the Spain star just 49 seconds to make his mark, a new fastest goal in Super Cup history.
Ever Banega had previously held the record, scoring in the third minute of play during the 2015 clash between Sevilla and Barcelona, with that game producing one of the best finals in the tournament's history as Barca recorded a 5-4 win after extra time.