Real held by promoted Levante
Real remained unbeaten, and had another clean sheet, but once again struggled to make their quality count, this time against a promoted club with a squad assembled on a shoestring.
The Madrid side slipped off the top of La Liga down to third place with 11 points from five games, two behind leaders Valencia and one short of champions Barcelona.
Valencia swept to a 2-0 victory at Sporting Gijon, while Barcelona beat 10-man Athletic Bilbao 3-1 away in a bruising encounter which also saw their striker David Villa sent off.
The match at the Ciutat de Valencia stadium was a David versus Goliath contest - the world's richest football club by income against a side who only came out of financial administration on Thursday.
Levante had leaked 10 goals in their first four games back in the top flight and packed the edge of their area, dragging Real into a niggly, stop-start affair.
A lively Cristiano Ronaldo had a powerful header saved by Levante goalkeeper Manuel Reina but although the visitors dominated possession they laboured to carve clear openings.
As Real's frustrations grew their doctor, Jose Carlos Hernandez, was sent to the stands for protesting about a foul on Ronaldo, and Reina pulled off some desperate late saves.
"The players showed the right attitude, it's just that last season we scored goals with relative ease and this year we seem to be anxious or feeling the pressure," Real director general Jorge Valdano told Spanish television.
Barcelona proved they could live without the injured Lionel Messi at San Mames as they quickly took control against a hard-running Bilbao side.
Villa had already hit the post when Bilbao defender Fernando Amorebieta's foot-up tackle on Andres Iniesta earned him a straight red card in the 34th minute.
The visitors struck the woodwork just after the restart but Barca made the extra man tell.
Seydou Keita slipped through on to Villa's pass to score in the 55th and Xavi fired in a deflected shot from outside the area after 74.
Villa was sent off four minutes from time after tangling with Carlos Gurpegi and Igor Gabilondo pulled one back for Bilbao. But as the hosts poured forward, Sergio Busquets settled the match after a swift Barca counter-attack.
Two quick goals from Mehmet Topal and Roberto Soldado gave Valencia a win at Sporting to set them up nicely for Wednesday's Champions League clash at home to Manchester United.
Turkish midfielder Topal headed in from a corner after only seven minutes and the impressive Juan Mata crossed for Soldado to stroke the ball home from close range three minutes later.
Mata and Manuel Fernandes bossed the midfield for the visitors and it was not until the second half that Sporting had a meaningful chance on goal when David Barral struck the post.