Real, who last dropped points against champions Atletico Madrid in mid-September, remain a point clear of Barcelona and have a game in hand.
Real Madrid took the lead against Valencia after Alvaro Negredo handled a Toni Kroos free kick in the penalty area and Cristiano Ronaldo coolly placed the spot kick into the corner with 14 minutes played.
An Andres Gomes shot deflected off Dani Carvajal and hit the post in first-half stoppage time as Valencia battled back. Antonio Barragan then saw a shot deflect in off Pepe in the 52nd before Nicolas Otamendi nodded home a corner after 65 minutes.
"We have to give credit to Valencia. They played their way back into the match and did well. It's sad that we have dropped three points and our run has come to an end but the league is long," Real defender Sergio Ramos told reporters.
Moyes’ Sociedad defeats Barca
Jordi Alba headed into his own net in the second minute to give Sociedad the lead against a Barcelona side with Lionel Messi and Neymar on the bench, having only returned on Friday from their Christmas break.
Barca failed to link up well in attack and it was David Moyes' side that carried the greater threat on the counter for much of the game. In the final stages, with Messi and Neymar on, Barca did begin to press but the San Sebastian hosts were resolute at the back.
"There is no point in saying what might have happened if they [Messi and Neymar] had started the game," said Barca coach Luis Enrique. "I thought it was the right decision as I didn't want to take a risk with the players who had just returned from holiday.
"I don't think the result was just, as we didn't deserve to lose, but this is football and it can happen that you don't get the luck when you need it."
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