Marco Asensio and Vinicius Junior scored second-half goals to earn Real Madrid a solid 2-0 win over struggling Valencia on Thursday as the visitors finished the match with 10 men.

Valencia defender Gabriel Paulista was shown a straight red 18 minutes from time for chopping down Vinicius with a wild tackle that almost started a brawl among players on the pitch.

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The LaLiga champions climbed to 45 points in second place in the standings, five behind leaders Barcelona. Valencia, who fired manager Gennaro Gattuso on Wednesday, are on a five-game winless streak and are 14th on 20 points, one clear of the relegation zone.

Madrid goalkeeper Thibaut Courtois was happy with the clean sheet and said he's seen improvement in the team's defence as they try to close the gap to leaders Barcelona.

"We've now kept three clean sheets in a row. But I'd have preferred to concede the other day and win [against Real Sociedad], the most important thing is always the three points," Courtois said.

"Defensively we've improved, in Bilbao and against La Real. Today they didn't have many chances. We did well. In the first half we didn't score but we did in the second, and with the sending off the last 15 minutes were easier."

Real, bidding to retain the title, are under pressure from their arch-rivals Barca who are unbeaten in their last 14 matches in all competitions and on a four-game winning streak in LaLiga.

They were the better side for large parts of the game and controlled the tempo on a chilly night in Madrid, but it took them a while to find their mojo in front of goal, with Vinicius and Karim Benzema wasting good opportunities in the first half.

Antonio Rudiger had a goal ruled out by VAR for a Benzema foul in the build-up just before half-time.

Real came out strong after the break and struck twice in two minutes, a magnificent curling shot into the top corner by Asensio after 52 minutes followed by Vinicius slotting home from close-range to finish off a lightning quick counter-attack.

The win came at a cost to Carlo Ancelotti's side, though, as both Eder Militao and Benzema were forced off with apparent injuries and were lucky that Vinicius was able to walk away from the wild challenge by Paulista.

"I don't know [about the red card], but we have to protect Vini. He's very expressive on the pitch, he takes players on and defenders don't like that," Courtois said. "It's typical. It's his technique, his way of playing, we need this Vinicius to open up defences.

"I think he's been kicked a lot and today I'm glad that a referee has been brave enough to send him off, the ball had gone, it made no sense. That has to be a sending off."

Real Madrid play Mallorca in LaLiga on Sunday and travel to Morocco on Monday for the FIFA Club World Cup.

"This is what happens when you play every three days," Ancelotti said of the injuries. "Militao is out for Sunday, but Benzema [injury] looks to be minor."