Andre Silva had a brace inside five first-half minutes, with Wissam Ben Yedder putting the game beyond doubt five minutes before half-time.
Sevilla went into the LaLiga clash on a high after a 5-1 demolition of Standard Liege in the Europa League a week previously and a 6-2 away win over Levante snapping a two-game domestic losing streak.
Silva capped off a fine counter-attacking move for the opener at the Ramon Sanchez Pizjuan Stadium and his second came on another break when Thibaut Courtois could only parry a shot into the Portuguese's path.
Quoted on the club's website, Machin said: "It's a night to enjoy and to remember. Those who do not beat Real Madrid many times will remember it, without a doubt. The crowd has enjoyed it since the first minute and until the end.
"It was a round night for the people of Seville to enjoy. (It is) a pity that it is not on a weekend so that the night can be extended."
Gareth Bale could only hit the post with a first-half shot, and a goal for the visitors from Luka Modric was ruled out by VAR for offside.
Real defender Marcelo, quoted on the club website, said: "You have to admit Sevilla were better in the first half. We got more of the ball in the second half but they were dangerous on the counter.
"In the second half, maybe if Luka's goal had stood, the game would have been different.
"If you lose, you drop three points and that can make the difference later in the season. We tried our best and let's see if we can avoid such errors in the future.
"We need to change things now, defeat hurts, but we have to pick ourselves up for the next game. I picked up a knock, but the defeat hurts more."