The attacking midfielder scored with a wonderful strike to put Real Madrid 1-0 up in the UEFA Super Cup tie against Sevilla.
The Frenchman confirmed that the 20-year-old will stay at the club this season and compete for a place in the side, rather than head out on loan.
"Asensio is going to stay with us. That's my plan," Zidane told 'Marca'.
"When you have to play, play well, and I am very happy with the work he has done.
"He had a complete game, not only for the goal".
Asensio's form could mean that James Rodriguez or Isco may leave the club given that first-team opportunities may be limited for the duo.