The La Liga champions took the lead in the 10th minute when Tiago headed past Iker Casillas from a corner, before Cristiano Ronaldo levelled from the penalty spot.
Arda Turan - one of the players to join the action from the bench - settled the derby when he swept in an effort 14 minutes from time.
And Simeone, who watched from the stands as he continued to serve a touchline ban, said Arda, along with fellow replacements Antoine Griezmann and Mario Suarez, were crucial to his side's success at Santiago Bernabeu.
"I think we started well in the first half and later I didn't like the way the team was playing," he said. "In the second half with Koke in the centre we had more control and Arda gave us more creativity and Griezmann more pace.
"The tactical changes worked very well and in the final 15 minutes we were playing in exactly the way we are looking to.
"What I am most pleased about today is that the players who came off the bench did what we were expecting of them and did it well."
Atleti visit Olympiacos in the UEFA Champions League on Tuesday.