Luka Modric's ball into the area deflected off two defenders into the path of Asensio, who fired a left-footed shot into the bottom-right corner of the net from 10 yards out.
Brazilian teenager Vinicius Jr. has been called into the Real Madrid squad for Saturday's La Liga game at home to Espanyol, taking the youngster closer to his debut for the European champions following his move from Flamengo.
Modric played a major role in Madrid's third successive Champions League success and Croatia's journey to the World Cup final in Russian Federation, winning the Golden Ball in the process.
'We are not going to win 5-0 every game, ' Varane said.
"We have to go into it naturally and make the best decisions in each game, knowing the strength in depth we've got at our disposal, more than ever". We will correct [mistakes], the important thing is to create 30 goal chances.
After an emphatic Champions League win over AS Roma on Wednesday, Lopetegui shuffled his pack for the visit of Espanyol, sixth in the table after a good start to the season.
Marco Asensio celebrates his winner
Said di Francesco: "I expected Real Madrid to be this good, they are a team of champions. These people who are complaining about me should be aware that if I had taken over the club, that if this was possible, then they would not have a voice today".
Los Blancos looked sharp on the ball and dominated possession but allowed Espanyol to break on the counter attack on several occasions.
"I would say it was nearly ideal, I'll keep the goal chances that we have created".
Further goals from Jonathan Calleri, Ibai and Burghi in the second half gave Alaves three more points to continue their impressive start to the campaign.
He said: "They are training brilliantly and competing very well". They played well, they're very well organized...
Roma may head to Spain on the back of just one Serie A win - and that on the opening weekend of the new season - but Lopetegui is expecting a stern test from the Italians. "As a coach he has entered history as one of the greatest at Real Madrid", he said.
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