Barcelona and Juventus maintained their league title charges in Spain and Italy with away wins on Sunday, when Liverpool and Manchester United had contrasting fortunes after being reduced to 10 men.
Veteran Juventus goalkeeper Gianluigi Buffon set another personal milestone, while 18-year-old French striker Ousmane Dembele also enjoyed a memorable day, and Hamburger SV eased its relegation worries in Germany.
Bayern Munich, Paris Saint-Germain and Leicester — the respective leaders in Germany, France and England — played already on Saturday.
A look at the action from Europe's major leagues on Sunday:
Lionel Messi continued his impressive form by scoring two goals in Barcelona's 4-0 win over Eibar, as the strike force of Messi, Luis Suarez and Neymar reached a total of 100 goals this season in all competitions.
It was the fourth goal, scored by Suarez after Messi's earlier brace, which brought up the scoring century.
Messi scored with a great run in the 41st and added a penalty in the 76th, leaving Barcelona with an eight-point advantage over Atletico Madrid, which later won 3-1 at Valencia to keep pace with 10 games to go.
Real Madrid stayed 12 points behind Barcelona after Saturday's 7-1 rout of Celta Vigo.
Also Sunday, Real Betis defeated visiting Granada 2-0, Athletic Bilbao won 2-1 at Sporting Gijon, and Real Sociedad drew 1-1 with last-place Levante.
Playing with 10 men proved to be no problem for Liverpool in the English Premier League, but the same could not be said of Manchester United.
Liverpool responded to James Milner's sending-off in the 62nd minute against Crystal Palace by coming from 1-0 down to win 2-1 as Christian Benteke's penalty clinched victory in the sixth minute of injury time.
United was made to pay for a 26th-minute red card to Juan Mata — also for two bookings — at West Bromwich Albion, which won 1-0 thanks to Salomon Rondon's goal.
United dropped three points behind fourth-place Manchester City in the race for Champions League qualification and is now only three ahead of Liverpool, which has won three straight league games for the first time in a year. City has a game in hand over United too.
Leicester beat Watford 1-0 Saturday to extend its lead to five points. Nine games remain.
Juventus restored its three-point lead over Napoli in Serie A with a 2-0 win at Atalanta, while Inter Milan boosted its chances of returning to the Champions League with a 3-1 win over Palermo.
Andrea Barzagli and Mario Lemina scored for Juventus while Gianluigi Buffon had a ninth successive clean sheet. The goalkeeper has not been beaten in Serie A in 836 minutes, the third-longest stretch in league history.
AC Milan could have leapfrogged fifth-place Inter, temporarily at least, but lost 2-0 at 10-man Sassuolo to end a run of 12 matches undefeated in all competitions.
Frosinone beat fellow struggler Udinese 2-0, and Genoa also boosted its chances of escaping the drop with a 1-0 win over Empoli. Carpi drew 0-0 at Bologna and Torino drew 1-1 against Lazio.
Nicolai Mueller scored twice as Hamburger SV eased its Bundesliga relegation fears with a 2-0 home win over third-place Hertha Berlin.
Hamburg climbed to 10th, seven points above Eintracht Frankfurt in the relegation playoff spot with nine games remaining.
Earlier, Darmstadt held high-flying Mainz to a scoreless draw that denied the home side the chance to go fourth. Mainz remained fifth, a point behind Schalke.
Bayern Munich preserved its five-point lead with an entertaining scoreless draw at Dortmund on Saturday.
Seven-time champion Lyon routed Guingamp 5-1 to move back to third while Marseille's poor home form continued as struggling Toulouse secured a 1-1 draw in the French league.
A week after Lyon ended leader Paris Saint-Germain's 36-match unbeaten run in the league, France striker Alexandre Lacazette confirmed his return to the form that made him the league's top scorer last season with a brace. Rachid Ghezzal and Maxwell Cornet also contributed for Lyon and an own goal from Reynald Lemaitre completed the rout.
Lyon now trails second-place Monaco by six points after the Principality side drew 2-2 at Caen on Friday. Runaway leader PSG has a 23-point lead.
The 18-year-old Ousmane Dembele scored his first hat trick as Rennes rose to fifth place with a 4-1 defeat of Nantes in the western derby.