Domingos Duarte then scored again for the visitors with 12 minutes left to make Madrid sweat but James Rodriguez made sure of victory three minutes into stoppage time.

Carvajal told reporters after the match: "I am thrilled for Hazard, it was a well-deserved goal, he is working well and getting better every time."

Carvajal has been filling in at left-back with Madrid suffering from injuries and the 27-year-old is happy to play anywhere.

He added: "The coach told me to play left-back because of injuries, I did it a couple of times last season and that's what he wanted me to do, but the important thing is the three points."

He hopes Real can tighten up at the back but is happy to see the club enter the international break at the top of the LaLiga table.

He said: "We can't let this keep happening at 3-0 up at home, we need to correct that because it will cost us points.

"Going ahead and them not being able to equalise is not a sign of strength. We need to be more convincing.

"Now we go into the break league leaders, regardless of what is happening the rest of the weekend. We can start to focus on a difficult week away from home."

Midfielder Federico Valverde echoed the sentiments of Carvajal and believes leading the league into the break gives the club something to build on.

Valverde said: "It's always important to win and it gives us massive motivation to stay top.

"I performed well today but there's much more to come from me, I have to keep improving and learning from my team-mates.

"Playing alongside any Real Madrid midfielder is a source of pride and satisfaction. The aim at this club is to fight for silverware on all fronts and do this badge really proud".