The Anadalucians had been 1-0 behind after the first leg but performed superbly at La Rosaleda to progress.
Isco netted the first goal for Malaga before half time and Roque Santa Cruz netted the crucial second.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.