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.
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.
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.
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.
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.
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.
