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Atletico, who have now lost six times this season, are second in the standings on 74 points after 36 matches, nine behind champions Barcelona.
The result was harsh on the home side, who largely dominated possession yet were unable to create clear-cut chances against Valencia, who sit 12 places and 16 points above them in La Liga.
Barcelona closed in on the La Liga title after beating 10-man Atletico Madrid 2-0 in Saturday's top-of-the-table showdown at the Nou Camp.
The hosts were galvanised and produced a bold and exciting display of counter-attacking football that made it easy to forget they have been struggling at the foot of the table for most of the season.
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.
Lionel Messi scored his 50th career hat-trick to fire Barcelona to a 4-2 win at Sevilla on Saturday after the champions had twice fallen behind.
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.
Real Madrid earned a therapeutic 2-0 victory at home to Sevilla with late strikes from Casemiro and Luka Modric as Santiago Solari's stuttering side leapfrogged the Andalusians into third spot in La Liga.
Real Madrid endured a frustrating start to the new year as they drew 2-2 at struggling Villarreal and were left seven points behind La Liga leaders Barcelona.