Real Madrid, who had no shots on target in the first half, spent most of the second half in panic mode, trying to avoid a huge defeat.
Nevertheless, once again a costly mistake gave Barcelona a chance to score. Substitute Dani Ceballos lost the ball in midfield and Gavi ran forward and crossed for Padry to head point-blank into an empty net.
Karim Benzema scored a consolation goal for Real in extra time, tapping home the rebound after Marc-Andre ter Stegen had his first effort denied.