Bale netted twice and provided two assists during the high-scoring clash at the Bernabeu.
Ancelotti is confident that the world's most expensive player is finally proving his worth following a shaky start to life in Spain.
"Tonight everyone saw the real Gareth," Ancelotti told reporters. "He played really well, showing fantastic skills.
"It takes time [to adapt] but it was a necessity. Now he doesn't have problems physically and he is improving his confidence, so he will be very important for us in the future."
Real are now third in the La Liga table, six points behind leaders Barcelona.