Argentina midfielder Perez started against the world and European champions just two days after he was unveiled as a Valencia player following his move from Benfica.
Real had won 22 competitive games in a row before facing Nuno Espírito Santo's side, but that national record run came to an end courtesy of goals from Antonio Barragan and Nicolas Otamendi after Cristiano Ronaldo's controversial penalty put Carlo Ancelotti's men in front.
Former Estudiantes man Perez played the full 90 minutes and revelled in a victory that leaves fourth-placed Valencia five points behind leaders Real.
He told the club's official website: "Everything worked out perfectly. I am very happy with my debut in such a big game. We put in a great performance, despite going behind early.
"We always kept the same attitude. Nuno knows me, he knows my positioning on the pitch and I am available to play wherever the team need me.
"These past few days have been very intense. Luckily everything was resolved and I was able to play. It was marvellous, like a dream. The fans were always behind us in this game as well, which is fundamental for turning a scoreline around.
"The fans here are amazing, so lets hope that they continue supporting us this way for the rest of the season."
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