Real Madrid lost its first home match this season 1-0 to Sporting Gijon on Saturday, inflicting a major setback to the host's hopes of catching Spanish leader Barcelona.
Barcelona moved eight points clear with a 1-0 win at Villarreal.
"The mathematicians say the league is not lost, but objectively, we can say that it is practically impossible," Madrid coach Jose Mourinho said.
The defeat was Mourinho's first at home in league play since FC Porto lost to Beira Mar 3-2 in February 2002.
Miguel de las Cuevas broke free on the edge of the area and fired in off the post for the winner in the 79th minute, then Sporting resisted a desperate late push to hand Madrid's first loss in 24 matches at Santiago Bernabeu Stadium this season.
At El Madrigal Stadium, Gerard Pique controlled a ball flicked on by Sergio Busquets with his chest that put him through the defense before rifling it past Villarreal goalkeeper Diego Alves for the 66th-minute winner.
Barcelona's 28th game without defeat broke a club record that had stood since the 1973-74 season.
Barcelona's 81 points in 30 weeks also set a league record.
The absence of the injured Cristiano Ronaldo, Karim Benzema, Marcelo and the suspended Xabi Alonso showed as Madrid struggled to create chances.
Madrid's Ricardo Carvalho had a goal disallowed two minutes in when the referee ruled the ball went over the byline.
After the early scare, Sporting quickly settled down in defense and frustrated the repeated incursions of Angel Di Maria down the left flank.
Madrid had to wait until the 35th for Di Maria to finally have a shot on target, but Sporting goalkeeper Juan Pablo Colinas was well-positioned to save.
Midfielder Sami Khedira sent his header well wide in a rare chance for the hosts right before halftime.
"We gave away the first half, we didn't do anything," said Madrid captain Iker Casillas. "It is a tough result to digest, (but) we have to pick ourselves up."
Madrid striker Gonzalo Higuain returned to the pitch for the first time since injuring his back last November in the 57th, and three minutes later tested Colinas with a hard strike inside the area.
But Madrid failed to react and De las Cuevas did not waste his chance to stun the Bernabeu crowd.
Down a goal, Madrid showered Sporting's area with crosses, but Colinas made a number of saves and the defense held firm.
"Football is about moments, and there are glorious ones," said Sporting coach Manolo Preciado, whose team's second away win of the season lifted it six points clear of the drop.
Former Real Madrid striker Ronaldo was honored before the match.
Barcelona was without suspended Xavi Hernandez, while defenders Carles Puyol, Eric Abidal, Maxwell and forward Pedro Rodriguez were sidelined for medical reasons.
Coach Pep Guardiola also left Lionel Messi out of the starting 11 and gave the nod to 19-year-old Thiago Alcantara and Ibrahim Afellay.
Villarreal was dangerous on the counterattack early and Barcelona goalkeeper Victor Valdes had to make a pair of excellent saves to deny Giuseppe Rossi in the 6th and 12th.
The Catalan side missed Messi's offensive punch more than Xavi's playmaking as it dominated possession but failed to generate clear-cut scoring chances.
The lack of precision in the area left Barcelona with a sole long strike from Adriano in the 39th as its only shot on goal in the first half.
Diego Alves swatted Andres Iniesta's strike over the crossbar in the 47th, and David Villa barely missed with a left-footed shot from the right two minutes later as Barcelona pressed to break through after the restart.
Messi went on in the 53rd for Seydou Keita, and Barcelona began to push Villarreal further back into its own area until Pique appeared to claim Barcelona's 13th win in 15 away games this season.
Diego Alves saved a well-placed Messi free kick and a long shot by Dani Alves in the last 10 minutes, while Valdes made a reflex leg save to block a close-range shot by Santi Cazorla in the 85th.
Elsewhere, Roberto Soldado scored four goals in the second half to rally Valencia to a 4-2 win at Getafe.
Manuel del Moral put Getafe ahead in the 23rd, but Soldado equalized one minute after the restart when he converted an excellent pass from Juanma Mata.
The former Getafe striker grabbed Valencia the lead in the 64th, and capitalized on a defensive error two minutes later to make it 3-1.
Soldado banged home his 10th goal of the season in the 77th before Adrian Sardinero pulled one back for Getafe in the 88th.
The victory pushed Valencia provisionally ahead of Villarreal into third place.
On Sunday, it's: Real Sociedad vs. Hercules, Espanyol vs. Racing Santander, Levante vs. Malaga, Deportivo La Coruna vs. Mallorca, Sevilla vs. Zaragoza, and Osasuna vs. Atletico Madrid.
Almeria hosts Athletic Bilbao on Monday.
Madrid plays Tottenham on Tuesday and Barcelona faces Shakhtar Donetsk on Wednesday in the Champions League.
