The English side came from behind to seize the initiative, Alexandre Lacazette scoring twice and Pierre-Emerick Aubameyang once.
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Arsenal will take a deserved lead to Valencia for the second leg thanks to Alexandre Lacazette's double and a late third from Pierre-Emerick Aubameyang.
The visitors started confidently and took the lead when Mouctar Diakhaby nodded in from a well-worked corner routine but Unai Emery's men turned the contest around within 15 minutes and held sway thereafter.
Lacazette levelled after a purposeful run and lay-off from Aubameyang then headed in Arsenal's second in the 26th minute. But the key moment in the game, and possibly the tie, may have arrived in added time when Aubameyang fired in from Sead Kolašinac's deep cross.
View from the stadium: Andy Brassell
Arsenal will be pleased after a pulsating first leg. They were in deep trouble in the early stages but came back with real fire – and Aubameyang's late goal, just as it looked as if a third would elude them, is vital. The fans were tense early on but as their team went from strength to strength, ended up creating the best atmosphere here in a European tie this season.
Man of the match: Alexandre Lacazette
The Gunners were slow out of the blocks but Lacazette turned the tide significantly in their favour. The French striker had the presence of mind to keep pace with Aubameyang and was rewarded with a tap-in from his strike-partner's pass.
His clever movement paved the way for him to head in the second and he should have completed his treble after the interval. Valencia simply had no answer to his pace and guile in the final third.
4: Four of Mouctar Diakhaby's five European goals have come in the UEFA Europa League knockout stages.
4: This is the fourth time Alexandre Lacazette has scored twice in a European game – all since February 2017.
10: Ten of Pierre-Emerick Aubameyang's last 12 European goals have come in home matches.
14: Arsenal have scored in their last 14 home games in all competitions, netting two or more in 13 of those matches.
What does it mean?
Arsenal's strong position in the tie is underlined by the fact they have progressed from nine of their last ten European knockout ties in which they have won the first leg. However Valencia, who have lost their only two previous UEFA Europa League semi-finals, have progressed three times in the knockout stages after losing the first leg – no club has a better record than that.
With two games to go in the Premier League Arsenal lie fifth, two points behind Chelsea. Failure to beat relegation-threatened Brighton at home on Sunday afternoon could end their top-four hopes.
Valencia also have aspirations of qualifying for the UEFA Champions League via the Liga but probably have to win their last three games to overhaul Getafe and Sevilla, starting with a trip to rock-bottom Huesca on Sunday evening.