In Spain, Messi appeared to be back to his best as he netted a hat trick to set another scoring record for Barcelona in a 7-0 win over Osasuna.
Here is a look at the action from the leading leagues in Europe on Sunday:
Liverpool routed soon-to-be-deposed champion Manchester United in a 3-0 victory at Old Trafford, with Steven Gerrard converting two penalty kicks and Luis Suarez also scoring in a one-sided match that highlighted the gulf that has emerged between the two opponents.
United striker Wayne Rooney called it ''a nightmare'' and ''one of the worst days I've ever had in football.''
Tomas Rosicky's goal after 72 seconds sent Arsenal to a 1-0 win at Tottenham. Arsenal and Liverpool are four points behind Chelsea, and both have a game in hand. Manchester City is six points behind, but with three games in hand.
Lionel Messi set another scoring record by netting a hat trick to pace Barcelona's 7-0 rout of Osasuna in the Spanish league, ensuring the defending champions stayed in striking distance of leader Real Madrid before their critical ''clasico'' match next week.
The three goals bring Messi's career tally for Barcelona to 371 in all games - including friendlies - breaking the club record of 369 held by Paulino Alcantara since 1927. The 26-year-old Messi was already the club's all-time leading scorer in official games.
Also, striker Imanol Agirretxe's second-half header gave Real Sociedad a 1-0 win at home over Valencia. Sevilla eased to a 4-1 win over Valladolid at home, while Real Betis drew 0-0 at Elche as it remained stuck at the bottom of the standings.
Andrea Pirlo's late goal saw Juventus maintain its charge to a third successive Serie A title as it beat Genoa 1-0 to extend its lead to 17 points.
Pirlo fired home a free kick two minutes from time as Juventus struggled to a victory after Gianluigi Buffon had saved Emanuele Calaio's penalty.
Third-place Napoli visits Torino on Monday and is seven points ahead of Fiorentina, which beat Chievo Verona 3-1.
Earlier, AC Milan fought back from two goals down but lost 4-2 at home to Parma after playing almost the entire match with 10 men.
Elsewhere, bottom club Sassuolo beat 19th-place Catania 3-1 and nine-man Livorno beat Bologna 2-1 in tense relegation battles.
Zlatan Ibrahimovic scored twice as Paris Saint-Germain beat Saint-Etienne 2-0 to retain its eight-point lead over Monaco at the top of the French league.
Ibrahimovic opened the scoring with a low strike in the 14th minute before volleying home to double the lead in the 41st for his 25th league goal this season.
PSG stretched its winning streak to seven games in all competitions.
Elsewhere, Dimitar Berbatov scored a goal and made two assists to lead Monaco to a 3-2 win over fifth-place Lyon. Montpellier secured a precious point in the battle for safety by salvaging a 1-1 draw with Bordeaux.
Hakan Calhanoglu scored in the 80th minute in a 2-1 victory for Hamburger SV over Nuremberg in a game between struggling Bundesliga clubs.
An own-goal by Mike Frantz in the 86th sealed Nuremberg's fate despite a goal in injury time by Josip Drmic. Hamburg goalkeeper Rene Adler saved the victory by turning away Jose Campana's free kick, the last shot of the game.
On Saturday, Bayern Munich extended its league record unbeaten run to 50 games and moved 23 points ahead of Borussia Dortmund with nine games remaining by beating Bayer Leverkusen 2-1.
Ajax played to a 0-0 draw at 11th-place NAC Breda, but the three-time defending champion leads the Dutch title race by seven points.
Dusan Tadic scored an injury-time winner to give FC Twente a 2-1 victory over AZ Alkmaar. It moved into second place on goal difference over Vitesse Arnhem, which lost 2-1 at home to PSV Eindhoven on Saturday.
Feyenoord beat Heerenveen 2-0 on goals by Ruud Vormer and Lex Immers. It is in fourth place, one point behind Twente and Vitesse.