As expected, it was the visitors that dominated the ball in the early stages, but Alaves were a threat in the final third, with Munir's movement in the final third causing Sergio Ramos and Raphael Varane problems at the heart of the Real Madrid defence.
The home side brought on Alfonso Pedraza for the final 25 minutes, and the former Leeds United winger nearly made an instant impact, only for his volley from the edge of the box to deflect onto Keylor's crossbar via Raphael Varane.
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However, he capped his league debut with a fine first-half brace, either side of Manu Garcia's goal.
Just three minutes later, however, Pacheco's punch to clear a corner dropped in front of Ceballos on the edge of the box, and the midfielder connected with his volley sweetly to restore Madrid's advantage just before the break. Marco Asensio played in Ceballos, who cleverly cut the ball back before finishing the chance for the lead.
Alaves, who came into the goal without a point or a goal this season, equalised through Manu Garcia's header. However, three minutes later, Ceballos again bring Madrid winning 2-1.
Cristiano Ronaldo is back, and played in the defeat against Real Betis, but will be hoping for more success this afternoon. Alaves, meanwhile, are next in La Liga action away to Levante next weekend.