La Liga leaders Real Madrid returned to winning ways after two defeats, making light of playing most of the second half with 10 men to triumph 3-0 at home to mid-table Espanyol on Saturday.
Barcelona's Lionel Messi hit his 400th career goal for the La Liga leaders.
Atletico Madrid failed to build on Wednesday's notable Champions League success against Juventus when they were beaten 3-1 at a resurgent Valencia in La Liga on Saturday.
Lionel Messi squeezed home a stoppage-time penalty to grab a 3-2 win for champions Barcelona at Valencia in a thrilling and controversial La Liga match on Sunday.
An extra-time goal from Roberto Firmino gave Liverpool a 1-0 victory over Brazil's Flamengo to win the Club World Cup at the Khalifa International stadium on Saturday. It is the first time Liverpool have won the competition, which features each continent's champions, and they became only the second English team to lift the trophy after Manchester United in 2008.
Real Madrid's stuttering run continued as they were held 1-1 at home by La Liga minnows Eibar on Sunday, drawing a fourth consecutive game in all competitions for the first time in more than a decade.
Valencia's Paco Alcacer, Dani Parejo and Pablo Piatti found the target as they took full advantage of the first-half dismissal of Malaga's Sergi Darder to win 3-0 at the Mestalla on Friday.
A late header by Imanol Agirretxe gave Real Sociedad, who are without a coach, a 2-1 victory over 10-man Atletico Madrid in La Liga on Sunday.
Barcelona came through a testing local derby at Espanyol, winning 3-0 to cling to their slender lead at the top of La Liga after rivals Real Madrid had set the challenge by beating Valencia 2-1 in the earlier kick-off.
Lionel Messi scored twice as La Liga champions Barcelona saw off a persistent Valencia side, who had Eliaquim Mangala sent off in the first half, to win 4-2 on Sunday and stay on the heels of leaders Real Madrid.
Carlos Vela helped Real Sociedad overcome a European hangover when he grabbed a second-half equaliser to earn a 1-1 draw at promoted Elche in La Liga on Saturday.
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.
Real Madrid brushed off the absence of Cristiano Ronaldo and Gareth Bale to beat Espanyol 2-0 away and maintain their 100 per cent start to the league season while matching the La Liga record of 16 consecutive victories.
Barca overcome solid Bilbao challenge to scrape through 1-0.
Barcelona's stuttering title bid suffered another setback when they lost 2-1 at home to Valencia on Sunday, while Atletico Madrid moved level on points with the La Liga leaders after a comfortable win over Granda.
Real Madrid's hopes of overhauling La Liga leaders Barcelona suffered a stinging blow when they were held to a 2-2 draw at home to Valencia.
Barcelona suffered a first home defeat of the season when they lost 3-2 against Valencia after finishing with 10 men in La Liga on Saturday, leaving the door open for Madrid rivals Atletico and Real to move above them.
Barcelona left it late to snatch a 1-0 win at Valencia on Sunday after Atletico Madrid's 2-0 victory at home to Deportivo La Coruna was overshadowed by the death of a visiting fan hours before kickoff.
US Open champions Marin Cilic and Serena Williams kicked off their China Open campaigns with straight sets victories against battling underdogs on Monday, but Rafael Nadal suffered defeat in a rare doubles outing on his return from injury.