Barcelona responded to their shock Champions League elimination to Roma by beating Valencia 2-1 on Saturday in a subdued atmosphere at the Camp Nou, setting a La Liga record of 39 games unbeaten and taking themselves a step closer to another title.

Luis Suárez gave Barcelona the lead after a quarter of an hour by meeting a delicious outside-of-the-foot pass from his former Liverpool team-mate Philippe Coutinho, scoring with one touch from close range.

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The record-signing Coutinho, who joined the club in a £142m deal in January, then delivered an outswinging corner from which Samuel Umtiti headed in a second in the 51st minute. His goal came shortly after Gerard Piqué had saved his blushes by clearing a shot off the line from the Valencia forward Santi Mina following a slip by the defender.

The captain Dani Parejo pulled a goal back for third-placed Valencia by squeezing an 87th-minute penalty under the Barcelona goalkeeper Marc-André ter Stegen, but the Catalan club withstood an exciting final spell to move effectively to within seven points of a 25th league title.

Ernesto Valverde’s side lead their nearest challengers, Atlético Madrid, by 14 points, with Diego Simeone’s team hosting Levante and fourth-placed Real Madrid visiting bottom-placed club Málaga on Sunday.

In the early game on Saturday, Sevilla drew 2-2 with Villarreal, who led through goals from Daniel Raba and Carlos Bacca. However, the game turned after a 76th-minute red card for Jaume Costa and Nolito and Steven Nzonzi scored to level things up. Wissam Ben Yedder also saw red for Sevilla in the 62nd minute.

Las Palmas remain deep in relegation trouble after Mikel Oyarzabal struck the only goal of the game to give Real Sociedad a 1-0 win. It gave Sociedad back-to-back league victories for the first time since August.

Deportivo La Coruña won 3-2 for the second successive week as they inflicted a rare home defeat on Athletic Bilbao to keep alive their survival hopes.

In Italy Internazionale missed out on the chance to move up to third place in Serie A as they were held to a goalless stalemate at Atalanta. A point takes Luciano Spalletti’s side level with Lazio and Roma on 60 points but Inter could have leapfrogged clear of both with victory in Bergamo.

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Earlier, Cagliari eased their relegation fears courtesy of Luca Ceppitelli’s late winner against Udinese. Kevin Lasagna gave Udinese an early lead at the Sardegna Arena after great work from Antonin Barak, but the hosts fought back to win 2-1, Leonardo Pavoletti levelling before the interval before Ceppitelli’s header six minutes from time completed the comeback.

Facebook Twitter Pinterest Bayern Munich’s title-winners salute the crowd at the Allianz Arena. Photograph: Anadolu Agency/Getty Images

In the Bundesliga Bayern Munich came from behind to beat Borussia Mönchengladbach 5-1 in their first Bundesliga match since being crowned champions.

Bayern’s manager Jupp Heynckes, who will be replaced by Eintracht Frankfurt’s Niko Kovac at the end of the season, rested several first-team players.

The visitors took full advantage early on as Josip Drmic gave them a ninth-minute lead. However, a double from Sandro Wagner turned the game on its head before half-time and Thiago extended the lead early in the second half. David Alaba smashed home a 20-yard effort after 67 minutes before Robert Lewandowski completed the rout with eight minutes remaining.

Kovac’s hopes of leaving Eintracht Frankfurt with Champions League football next season were dealt a blow with a 4-1 defeat at Leverkusen. Kovac has four more league matches remaining, but he was unable to stop Leverkusen strengthening their grip on a Champions League place as a second-half hat-trick from Kevin Volland sealed victory for the hosts.

Leverkusen stay fourth in the Bundesliga, now five points ahead of their opponents as well as Hoffenheim, who moved above Frankfurt on goal difference after first-half goals from Serge Gnabry and Adam Szalai gave them a 2-0 win against struggling Hamburg.