The Portuguese international was the star - netting a treble in just 15 minutes, as Mourinho's men secured a valuable win against Pellegrini's expensively-assembled side
Cristiano Ronaldo netted a hat-trick while Gonzalo Higuain also on the scoresheet as the away side blew their hosts away with a blistering opening 45 minutes.
Both sides had early shouts for penalties for fouls on first Ronaldo and then Malaga's Joaquin. Neither prompted a reaction from the referee Antonio Miguel Mateu Lahoz however, despite the protests of players from both sides.
It was not long before Madrid took the lead. Gonzalo Higuain opened the scoring for the visitors with a cool finish from a tight angle after being played in by the impressive Angel Di Maria.
Madrid began to exert more and more pressure on the Malaga back-line and added a second goal after 24 minutes. Di Maria was the provider once more, this time for Ronaldo. After being found down the right-hand side the Argentine cut back on to his favoured left foot before whipping a tantalising ball into the area which left Ronaldo with the simplest of finishes from five yards out.
Ronaldo made it 3-0 around the half hour mark, dancing past a couple of Malaga players before dispatching a fine low strike from the edge of the area that gave Ruben in the Malaga goal no chance.
Clearly determined not to be outdone by the free-scoring Higuain of recent weeks Ronaldo soon made it 4-0, completing his hat-trick whilst doing so. His third was the pick of the bunch, a wonderful back-heeled volley that a bewildered Ruben in the Malaga goal could do nothing to stop.
Casillas came to the rescue once more just before half-time for Madrid, rushing out from his goal to make a terrific save at the feet of the on-rushing Joaquin.
Malaga came within inches of pulling a goal back just minutes into the second half when Joaquin struck a fabulous free-kick onto Casillas' crossbar.
Casillas pulled off another world-class save, this time from Eliseu, before Rondon then flicked an effort over the Spanish international as he came racing out of goal only to see his shot land agonisingly the wrong side of the post.
Malaga continued to push forward in search of goals, Sebastian Fernandez hitting the woodwork with a fine half-volley that had Casillas well-beaten. Despite this the scoreline remained the same, with Madrid running out 4-0 victors.
The home-side made a mockery of their performance in the first-half with some wonderful play in the second but by that time the damage was already done. Madrid dominated the first 45 minutes, scoring four times which then allowed them to ease off in the second half.
Mourinho will be happy with a win that puts his side top for the time being, while Pellegrini will take solace from his side's performance in the second half and will look to get their quest for Champions League qualification back on track against Rayo Vallecano on Wednesday night.