Following their weekend win against Espanyol, Madrid were hoping to consolidate their spot at the top of La Liga with a victory at the Ramon Sanchez Pizjuain.
Rivals Barcelona just before the Real Madrid game and victory would have put the reigning European champions on top of the league.
Sevilla however were not to be pushovers as they scored six against Levante in their last fixture.
Jesus Navas and his teammates started at a high tempo with transition into counter attack to find Portuguese striker Andre Silva who scored two goals in quick succession.
Wissam Ben Yedder scored the third goal of the encounter when he latched on to a rebound just before the half time break.
Speaking after the game Real Madrid coach was not impressed with the showing in the first half but urge his players to bounce back in their nest league game against title and derby rivals Atletico Madrid.
said, "We had a bad first half, Especially a bad start, when they scored two goals and set the tone for the game.
"We have to pick ourselves up, we have another important game in three days so we congratulate Sevilla and recognise we have not played how we wanted."
Real Madrid resume action in La Liga at home against city rivals Atletico Madrid on Saturday, September 29.