The draw came days after Real had won 5-0 at the same stadium against the same team.
They win 3-1 on aggregate, although Fabio Contreao and Angel di Maria were both sent off.
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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.