Valencia came from behind to snap Real Madrid's winning streak at 22 games, however Barcelona failed to take advantage as they lost 1-0 at David Moyes's Real Sociedad on Sunday.
Jordi Alba's early own goal was enough to consign Barca to defeat after coach Luis Enrique had left Lionel Messi and Neymar on the bench.
Earlier, Cristiano Ronaldo's first-half penalty looked to have Madrid on course to start the new year as they finished 2014, but Valencia roared back after the break with goals from Antonio Barragan and Nicolas Otamendi to move above Sevilla into fourth.
It is the first time since April 30, 2011 that both Madrid and Barcelona have lost on the same day and means Los Blancos retain their one point lead over the Catalans and Atletico Madrid having also played one game less than their title rivals.
"We had lots of chances. We started badly with an own goal and that punished us in the end, but we didn't deserve this result at all," said Barcelona midfielder Xavi Hernandez.
"It is a lost opportunity. We have started the year badly, but we will keep going."
Real Madrid boss Carlo Ancelotti also lamented the chances missed by his side at crucial points in the game at Mestalla.
"I don't think we deserved to lose," said the Italian.
"We just didn't have the luck to score when we had the chances to make it 2-0, then to go ahead 2-1 and finally at the end when we had many chances to make it 2-2."
Despite a bright start Valencia had to come from behind when Alvaro Negredo handled Gareth Bale's flick on from Toni Kroos's free-kick and Ronaldo duly stepped up to fire home his 33rd goal of the season from the penalty spot.
The World Player of the Year should have doubled his tally and his side's lead 12 minutes later when Bale's deflected cross fell perfectly into his path, but after rounding Diego Alves, Ronaldo could only turn the ball into the side-netting with the goal gaping.
Valencia also started the second-half in the ascendency as Andre Gomes sent a thunderous volley inches wide, but they were finally rewarded when Pepe turned a low drive from Barragan past the helpless Iker Casillas.
- Messi, Neymar on bench -
Bale had a great chance to restore Madrid's lead when he galloped in behind the Valencia defence seven minutes later, however the Welshman was denied by a fine saving challenge from Otamendi.
And just moments later, the Argentine centre-back was the star at the other end of the pitch as he towered above Ramos to power a header high past Casillas.
Madrid rallied in the final 15 minutes, but couldn't find an equaliser as Ramos sent a header inches wide before Alves denied Isco with a brilliant save from point-blank range and Otamendi cleared the danger before a Madrid player could pounce on the rebound.
Barca boss Enrique's huge gamble to leave Messi and Neymar, amongst nearly 300 million euros of talent on the bench, took fewer than two minutes to backfire in San Sebastian as Alba stretched to reach Sergio Canales's cross but could only turn the ball into his own net.
Without their other two South American stars, Luis Suarez ploughed a lonely furrow up front.
However, even he was ineffective as the visitors' best two efforts before the break came from Pedro Rodriguez who fired over before Geronimo Rulli bundled a low drive to safety.
Canales could even have added to the Basques' half-time advantage as he left Martin Montoya in his wake with an outrageous piece of skill only to see the former Sociedad 'keeper turn his effort behind for a corner.
Messi was introduced at the break and Neymar soon followed as Barca improved in the second period, yet they were denied by some dogged defending and even better goalkeeping from Rulli as he made two outstanding saves from Suarez in the final five minutes to prevent Barca snatching a point.