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.
Sevilla are now level with Real on 15 points and only trail the Madrid side on goal difference.
GUNS BLAZING
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.
Roared on by about 45,000 vociferous fans, the home side put early pressure on the Real goal and the pacy Navas caused havoc down the right flank.
He timed his run to perfection to outjump Marcelo and power Fernando Navarro's cross past Casillas for the opening goal.
Tempers frayed just before halftime when Guti and Didier Zokora squared up and Guti had to be restrained by team mates after he was barged by Perotti in the melee.
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.
Real director general Jorge Valdano said Casillas had saved the visitors from a heavier defeat.
"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."
MISERABLE START
Villarreal continued their miserable start to the season when they were held to a 0-0 draw at home by 10-man Espanyol earlier on Sunday.
A frenetic 2-2 draw between Real Valladolid and Athletic Bilbao saw the hosts finish with nine men and the visitors with 10.
Athletic striker Fernando Llorente was taken to hospital for tests after he received a blow to the head in the first half but the injury did not appear too serious and he was due to return to Bilbao on Monday.
Valencia climbed to fifth on 11 points after substitute Nikola Zigic pounced on a defensive error just after the hour mark to secure a
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