Real slumped to a 1-0 defeat at Athletic Bilbao on Saturday to remain on 41 points after 18 matches, five behind undefeated champions Barcelona, who took full advantage of Real's slip-up by thrashing Sevilla 4-0 at the Nou Camp.
Valencia have 38 in third and Real Mallorca leapfrogged Deportivo La Coruna into fourth with a 2-0 home win over the Galicians earlier on Sunday.
Atletico Madrid continued their recovery from a poor start to the campaign with a nervy 3-2 win over Sporting Gijon and Racing Santander's 18-year-old midfielder Sergio Canales cemented his status as La Liga's rising star when he netted the equaliser in a 1-1 draw with Real Valladolid.
Ever Banega laid the foundation for Valencia's third straight league win when the Argentine midfielder swept the ball high into the net in the sixth minute at the Mestalla, his first goal for the club.
Villa doubled the lead from the spot in the 28th after he was hauled back by Kiko and the referee awarded a penalty and showed the Villarreal defender a straight red card.
A defensive howler from Joan Capdevila gifted a third to his Spain team mate David Silva on 56 minutes and Nilmar pulled one back for the visitors with 29 minutes left after a mix-up between defender Alexis Ruano and goalkeeper Cesar Sanchez.
Silva crossed for Villa to score his 14th of the season at the death, putting the Spain striker back at the top of the La Liga scoring chart level with Barca forward Lionel Messi.
TENSE FINALE
Atletico had been lifted by a stirring comeback against second division Recreativo Huelva in the King's Cup on Thursday and carried the momentum into the match at their packed Calderon stadium earlier on Sunday.
Uruguay striker Diego Forlan raced clear to give them the lead in the 13th minute but the good work was undone 20 minutes later when goalkeeper Sergio Asenjo clumsily felled Diego Castro in the penalty area.
Castro picked himself up and sent Asenjo the wrong way to restore parity before Forlan nodded the ball into Assuncao's path for the Brazilian midfielder to poke home in the 53rd.
Teenage substitute Ibrahima Balde netted with an angled strike with 24 minutes remaining to make it 3-1 before Luis Moran scored in added time to set up a tense finale.
"We suffered unnecessarily at the end but these are three very important points," Atletico coach Quique Sanchez Flores said at a news conference.
"The positive results have had an impact and the players have more confidence and believe in what they are doing."
Racing teenager Canales followed up last weekend's two stunning strikes against Sevilla with another coolly executed chip to salvage a home draw against struggling Valladolid after Pablo Pinillos had scored in his own net in the 19th.
