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Los Blancos effectively settled the contest in a blistering ten-minute first-half spell, starting when Jude Bellingham opened the scoring in the 19th minute with a brilliant solo run through two defenders.
Bellingham then forced a second goal seven minutes later after his headed rebound bounced in off Malaga goalkeeper Alfonso Herrero following a save from Kylian Mbappe.
Mbappe added a third just before halftime with a sharp volley from a Trent Alexander-Arnold cross—his fourth goal of the campaign—before substitute Arda Guler tapped in a late fourth from a Vinicius Junior assist.
Mourinho rotated his lineup by making five changes, handing first starts of the season to new arrivals like Alexander-Arnold and Marc Cucurella.
While Malaga threatened briefly before the break through Rafa Rodriguez and Chupe, Real Madrid controlled the tempo in the second half to secure their first clean sheet of the season.
Bellingham received a standing ovation when substituted, noting afterward that he is thoroughly enjoying his attacking midfield role under Mourinho.
The win temporarily lifts Real Madrid ahead of reigning champions Barcelona, who host Rayo Vallecano on Monday.