Jude Bellingham and Kylian Mbappe were both on the scoresheet as Jose Mourinho’s side secured a third consecutive league victory.
Madrid took control of the game in the first half, scoring three goals within a 10-minute spell to put the visitors under heavy pressure.
Bellingham broke the deadlock after 19 minutes with a brilliant individual effort, weaving past two defenders before firing the ball through goalkeeper Alfonso Herrero’s legs.
The England midfielder was involved again seven minutes later when Herrero initially stopped Mbappe’s effort. Bellingham headed the rebound towards goal, forcing Malaga defender Carlos Puga to attempt a desperate clearance.
The ball, however, struck Herrero and went into the net for an own goal.
Mbappe then added Madrid’s third with a superb volley from Trent Alexander-Arnold’s cross, taking his tally to four goals for the season and moving him to the top of the league’s scoring charts.
Malaga came close to reducing the deficit before the break, with Rafa Rodriguez hitting the post following a corner routine, while Chupe sent another effort narrowly wide.
Madrid controlled proceedings after the interval and came close to extending their advantage when Bellingham struck the outside of the post.
The home side eventually found a fourth goal late in the match when Vinicius Junior set up substitute Arda Guler, who finished from close range.
Bellingham received a standing ovation from the Bernabeu crowd when he was substituted in the second half.
Reflecting on his role under Mourinho, Bellingham said he had been enjoying the freedom to move higher or deeper depending on the team’s needs.
Mourinho, meanwhile, praised his players for managing the second half effectively and highlighted the importance of recording their first clean sheet of the campaign.
Elsewhere, Deportivo La Coruna recorded their first victory of the season with a 3-1 win over Valencia, with Pierre-Emerick Aubameyang scoring his third goal of the campaign. Deportivo also benefited from own goals by Cesar Tarrega and Mouctar Diakhaby.
Athletic Bilbao also secured their first league win, defeating Celta Vigo 2-0 through goals from Alex Berenguer and Robert Navarro.
Defending champions Barcelona are scheduled to face Rayo Vallecano on Monday as they look to maintain their perfect start to the campaign.
