Winger Jesus Navas leaped superbly to nod the home side in front after 33 minutes and midfielder Renato also struck with a header in the second half to secure the surprise victory.
Real goalkeeper Iker Casillas had produced two stunning saves to deny Renato and Diego Perotti before Pepe equalised for the visitors with a powerful header just after halftime.
Manuel Pellegrini's expensively assembled Real side, missing the injured Cristiano Ronaldo for their first major test of the season, remain on 15 points from six matches.
On Saturday, Pedro's stunning strike gave Pep Guardiola's Barcelona side a 1-0 home win over Almeria as they equalled their best league start with six wins in six to reach 18 points.
The match at the Sanchez Pizjuan was billed as a test of Sevilla's ability to challenge the dominance of Barca and Real and Manolo Jimenez's players came out with all guns blazing.
He timed his run to perfection to outjump Marcelo and power Fernando Navarro's cross past Casillas for the opening goal.
Sevilla should have been at least two goals ahead at the break but Casillas somehow kept out Brazilian Renato's bullet header and he saved Real again immediately after halftime when it seemed easier for Perotti to score.
Pepe rocked Sevilla with a fine header from Guti's freekick in the 49th to level the scores but the home side poured forward and it paid off when Renato rose unmarked to glance in Adriano's cross in the 66th to secure a thoroughly deserved victory.
"We lost to a very good Sevilla," he said in a television interview. "They have been a very complete team for years and have a great support."
