La Liga leaders Real Madrid dropped points at home for only the second time this season.
Seven times reigning winner Lionel Messi was not nominated for this year's Ballon d'Or for the first time since 2005 and nor was his Paris Saint-Germain team mate Neymar.
In other matches, super-sub Messi helped Barca romp past Atletico
Barca dominated possession and Luis Suarez had several early chances but it was Villarreal who took the lead with Denis Cheryshev redirecting a Mario Gaspar shot past keeper Claudio Bravo on the half hour.
Barcelona's advantage over Real Madrid at the top of La Liga was cut to five points when they surrendered the lead and were held to a 1-1 draw in a thrilling clash at battling Sevilla on Sunday.
Real Madrid have reluctantly agreed to play their La Liga match at Rayo Vallecano at 1745 GMT on Monday, a day after the game was abandoned because of alleged lighting sabotage at Rayo's Estadio de Vallecas stadium.
Beat Real Madrid's unbeaten run in the 1988-89 season, and thump Rayo Vallecano 5-1
Rampant unbeaten leaders Barcelona ended the first half of the La Liga season with a record 55 of a possible 57 points when Lionel Messi scored one goal and had a hand in two more in a 3-1 win at Malaga on Sunday.
Barca said the move was part of their efforts to bring soccer and music together.
Atletico Madrid kept pace with leaders Barcelona and restored their five-point lead over third-placed city rivals Real when Diego Costa and David Villa each scored a penalty in a 2-1 win at Granada in La Liga on Thursday.
"We are really pleased and we just have to enjoy it," Celta defender Gustavo Cabral told Spanish television.
Barcelona forward Lionel Messi set a La Liga record of 253 goals when he grabbed a hat-trick in Saturday's 5-1 win at home to Sevilla, the latest milestone for the four-times World Player of the Year.
Lionel Messi wasted little time in finding his stride as he struck twice to lead 10-man Barcelona to a 3-0 home win over Elche and hand new coach Luis Enrique a happy start to the La Liga season on Sunday.
Champions Barcelona suffered a humiliating 2-0 home defeat to Hercules on Saturday when Nelson Valdez struck twice to give the tiny promoted club a shock La Liga victory at a stunned Nou Camp stadium.
Diego Costa scored twice as Atletico Madrid beat Valencia 3-0 to maintain their winning home run this season and keep pace with Barcelona at the top of the La Liga table.
Barcelona's bid for a fourth straight La Liga title is foundering due to their erratic away form but Tuesday's 3-1 Champions League victory at Bayer Leverkusen suggests they are unlikely to suffer the same problem in Europe.
Casemiro headed an 89th minute winner to earn Real Madrid a barely deserved 2-1 victory at Las Palmas in La Liga on Sunday as they closed the gap on second-placed Atletico Madrid to four points.
Saudi clubs have spent more than 400 million euros ($439 million) in the close season to sign players from Europe's elite teams.
Real Madrid conceded a late freekick to draw for the second time in four days as they were held 1-1 at struggling Villarreal, cutting their lead at the top of La Liga cut to six points on Wednesday.
Cristiano Ronaldo kept up his rich La Liga scoring form as Real Madrid beat Villarreal 2-0 on Saturday to move up to fourth.
Barcelona stayed hard on the heels of La Liga leaders Real Madrid when Lionel Messi's brilliance lifted a side containing several youngsters from the club's B team to a 2-1 win at home to Real Sociedad on Saturday.
Another win would confirm that Barca are heading in the right direction after pushing the reset button following the loss of Lionel Messi in the close season due to their financial problems.
Barcelona slipped five points behind La Liga leaders Real Madrid when Alvaro Vazquez netted a shock late equaliser to snatch a 1-1 draw for Espanyol in the Catalan derby on Sunday.
Barcelona failed to capitalise on Real Madrid dropping points against Villarreal as the La Liga champions were held to a 1-1 draw at home to Atletico Madrid on Wednesday, while talisman Lionel Messi limped off with a groin injury.
Real Madrid climbed back above Barcelona to the top of La Liga when goals from former Liverpool pair Xabi Alonso and Alvaro Arbeloa helped them to a stirring 3-2 comeback win over Atletico Madrid on Sunday.
Rafael van der Vaart admitted to handling the ball in the lead up to Real Madrid's opening goal in their 3-1 victory over Sporting Gijon in La Liga on Saturday.
Sevilla's devastating display to dispatch Malaga 4-1 on Saturday put them in their highest league position after 16 games for a decade and left little doubt that hiring coach Jorge Sampaoli to succeed serial winner Unai Emery was the right choice.
The Italian said he would avoid big changes to his team this time, after he tested midfielder Luka Modric up front in place of then-injured striker Karim Benzema in the last El Clasico in March, only to get hammered 4-0 by the Catalans.
Premier League clubs spend $1 billion for first time in January transfer window
Barcelona signing Robert Lewandowski is relishing a new challenge after joining the Catalan club and the 33-year-old said he was ready to play in their upcoming pre-season game against rivals Real Madrid in the United States.
Real Madrid are comfortably perched on top of the La Liga standings with 66 points while Barca are now third on 54 points with a game in hand, three points behind second-placed Sevilla.
Arsenal sailed through the Europa League group stages, winning five of their six group matches and take on Sporting next, who overcame Denmark's FC Midtjylland in their playoff.
English Premier League leaders Manchester City and Chelsea slugged out a magnificent 4-4 draw at Stamford Bridge.
A late double from Cristiano Ronaldo put some gloss on a stuttering performance from Real Madrid as they beat Celta Vigo 3-0 to cut the gap at the top of La Liga to five points.
Atletico Madrid made a typically aggressive start to lay the foundations for a 2-0 victory at home.
Leaders Barcelona played out a second straight 0-0 draw in LaLiga after mid-table Getafe battled for a home point in a hard-fought game on Sunday.
India are struggling to find a batter for the No. 4 slot, something that has also troubled them in the previous edition in 2019 in England.
Barcelona's 2-1 loss at Ajax Amsterdam in the Champions League last week was down to a lack of intensity while Sunday's 1-0 reverse at Athletic Bilbao in La Liga exposed their relative physical frailty.
Images from the La Liga matches played across Spain on Saturday.
Barca must beat Villareal on the weekend if they are to stand a chance of overhauling Real in the run in.