Casemiro headed in the first goal on 13 minutes and Karim Benzema doubled the lead on 41 minutes.
Eden Hazard was excellent in the first half and may be credited with an assist as he tried to flick the ball through to Benzema.
But there was no doubt about his involvement in the third goal, as he scored from Toni Kroos’ assist.
Alaves were brighter in the second half and Joselu pulled a goal back with a powerful header on 59 minutes.
But Benzema raced away to get his second of the game and the fourth for Real Madrid and put the result beyond doubt.
The result was the perfect way to help Real Madrid forget the midweek Cup exit against third-tier Alcoyano.
“It was what we needed after a difficult week. We want to win every game but every game is difficult,” Benzema said.
“This will be good for confidence and there is still a long way to go in the season.”
For Alaves it was not the way they wanted to celebrate the club’s 100th birthday.
Coach Abelardo Fernandez said: “We disappeared as a team after the first goal. At least there was a reaction in the second half.”
Earlier Saturday, Youssef En-Nesyri scored his second hat-trick in the space of a month to give Sevilla a 3-0 win over Cadiz.
The victory lifts the home side to third in the table and means that with 12 goals, En-Nesyri is current top goalscorer in the Spanish top-flight.
He got his first on the rebound after Suso’s shot had come off a post on 35 minutes.
He doubled the lead heading in a Suso free-kick on 39 minutes, and he nodded in the third from close range on 62 minutes.
“I have not changed anything, this is just the result of hard work and focus,” said the Morocco international, who has now scored hat-tricks in consecutive home matches.
He managed to net the second in spite of having needed treatment a moment earlier because of an eye problem.
“I couldn’t see properly out of one eye. But I knew the cross was for me and so I had to try to finish it. I scored the goal with one eye,” he said.
Sevilla coach Julen Lopetegui said: “I’m pleased for him and I’m pleased for the team. The attitude and the mentality of the team was excellent.”
Lopetegui will also be pleased En-Nesyri, who was linked with a move to West Ham in the transfer window, has no plans to move on.
The 23-year-old striker added: “I want to finish the season at Sevilla. This is a great club and I am very happy here.”
Also on Saturday, Huesca drew 0-0 with Villarreal and Real Sociedad drew 2-2 with Betis.
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