Antonio Rudiger's second-half goal earned LaLiga leaders Real Madrid a 1-0 home win over Mallorca on Wednesday, extending their unbeaten league run to 13 games.

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Centre-back Rudiger broke the deadlock in the 78th minute as he capitalised on some sloppy defending from a corner to power a header into the top corner and score his first goal of the season.

"Great cross by Luka, great block by [Dani] Carvajal and luckily it went in," Rudiger told reporters. "I'm happy because it was an important goal and three important points for us. This team has something special, a good mix of young and old talent."

Mallorca had mounted a resilient defensive display and came close to shocking Madrid with two efforts that hit the woodwork.

Vinicius Junior also went close to scoring on his return to action after being sidelined with an injury, but Mallorca keeper Predrag Rajkovic made a superb save to deny the Brazilian in the first half.

"It's always a difficult game when you come back from holidays," Carvajal told Real Madrid TV. "Mallorca played a tactically very good game, very aggressive in defence. The set piece gave us the victory.

"We close the first half of the season as possible leaders, 48 points is a lot. In the second half we'll be looking to surpass them."

Madrid next visit fifth-tier Arandina in the first round of the Spanish Cup before taking on Atletico Madrid in the Spanish Super Cup.