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Real moved on to 60 points after 31 games thanks to the victory but remain third in the standings.
Madrid are stuck in third on 57 points, 13 behind La Liga leaders Barcelona and five behind city rivals Atletico Madrid.
Arsenal became only the second team in Europa League history to win a tie after losing the first leg 3-1.
Valencia reached the final for the first time in 11 years by beating Real Betis 1-0.
A clinical Barcelona won 3-0 at Real Madrid in an intense second leg of their Copa del Rey semifinal as a Luis Suarez double helped them secure a 4-1 aggregate victory and a spot in the final for the sixth straight season.
A clinical Barcelona won 3-0 at Real Madrid in an intense second leg of their Copa del Rey semi-final on Wednesday.
Inter Milan, the winners of three European Cup and UEFA Cup titles apiece, also strolled through with a 4-0 home win over Rapid Vienna which completed a 5-0 dismissal.
Visitors Chelsea desperately needed a response after back-to-back humiliating away losses, with last Sunday's 6-0 thrashing by Manchester City following a 4-0 reverse at Bournemouth.
Messi, who suffered a thigh injury at the weekend against Valencia, appeared for the final half hour but could not help champions Barcelona find a late winner.
Madrid join Barcelona, Real Betis and Valencia in the semifinals.