Having lost last week’s first leg 3-2 in Barcelona, they won 2-1 with a goal in the last minute of the game last night.
That sent them through on away goals, the second time a team from the third tier has reached the last four, and are likely to face Athletic Bilbao next.
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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.