Andre Silva scored twice in the first 21 minutes – converting a Jesus Navas cross and then firing home a rebound after Navas’ shot was saved.
Gareth Bale hit the post and Sevilla’s Franco Vazquez struck the bar at 2-0.
Wissam Ben Yedder volleyed home a third to wrap up the game before half-time – his sixth goal in three games.
It was Real’s first league defeat this season under Julen Lopetegui and they were deservedly beaten – and never looked like threatening a comeback.
They had 21 shots, but it was quantity over quality, with Bale their only impressive attacking player – although he squandered several good chances to score.
Luka Modric, who was named the world’s best male player at the Best Fifa Football Awards on Monday, also had a goal disallowed by VAR for offside in the second half.
Sevilla, who beat Real 3-2 in their last meeting in May, looked very sharp and could have had more goals on the counter-attack as Real pressed forward.
Real had hoped to take advantage of Barcelona’s shock 2-1 defeat at bottom-of-the-table Leganes earlier on. Surprise package Alaves have the opportunity to join the two rivals on 13 points at the top of the table if they beat Getafe on Thursday.