Kepa Arrizabalaga was the hero as the goalkeeper saved two penalties following his introduction to the match.
Speaking after the match, the Chelsea boss gave his assessment of the game.
Hakim Ziyech gave Chelsea the lead in the first half before Gerard Moreno equalised for the Spanish side.
The match went into extra time and Chelsea began to dominate after a timid second half and the game was decided on penalties, with Kepa replacing Edouard Mendy for the shootout.
Speaking on the victory, Tuchel said: “It was tough, 120 minutes out of more or less nothing. We were very strong in the first 30/35 minutes. We lost a bit easy balls after our goal.
“Second half we were too passive, they equalised and deserved. We gave everything til the 120 minute. We deserved to win.”
Tuchel also gave an update on goalscorer Ziyech, who went off injured late into the first half.
The Blues will face Crystal Palace in the Premier League opener on Saturday, with the Super Cup win providing the squad with a mental boost going into the season.