Simeone's side scored their first opportunity of the second half, too, as just four minutes in Saul Niguez was quickest to a loose ball near the halfway line, and within seconds Koke released Griezmann to exquisitely lift the ball over Steve Mandanda and into the net.
It may have been Griezmann's parting gift amid Barca's interest in the France global forward, who opted to remain in Madrid for the 2017-18 season despite Manchester United's efforts to lure the 27-year-old to the Premier League.
"It's more than about winning the Europa League tonight, it's about more than a trophy", Atletico Madrid coach Diego Simeone said. He will spearhead the attack alongside Diego Costa. We will try again next year. Having confirmed last month that he would leave the club for a second time, it was the last opportunity for him to win a major trophy with them.
"Let's hope today's performance convinces him to stay there".
This will be the first meeting between Marseille and Atlético Madrid in European competition since 2008/09, when the Spaniards went unbeaten against them in the Champions League group stage (W1 D1).
Atletico, who are now second in the La Liga standings with a single match to play this season, are two-time Europa League winners, having tasted victory in 2009/10 and 2011/12.
Marseille continued to dominate for much of the first half, however, they were unable to take control of the tie as Jan Oblak was equal to much of the Ligue One sides efforts.
"It is never good to make comparisons".
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Gabi then wrapped up the scoring late on, and celebrated like a man who would prefer to forget he called this competition "s--" when his side dropped into it from the Champions League last December.
"I think the expectation in Marseille and across the country is quite extraordinary and our motivation comes from that", said Dimitri Payet, who is confident of beng fully fit after a minor muscle injury.
Atletico Madrid celebrate their Europa League victory against Marseille. And once that goal went in, it suddenly looked like a mammoth task for Marseille as we all know how sturdy the Atletico Madrid defence can be.
"This cup has given us a lot", he commented. "We want to enjoy the moment, let our hair down". Right-back Bouna Sarr has an issue with his shoulder but could be fit, with Hiroki Sakai likely to take his place if not.
Meanwhile, authorities in Lyon are hoping the match, which will kick off at 8:45pm (1845 GMT), will not be marred by violence.
They vastly outnumbered Atletico's fans inside the Stade de Lyon and made a nuisance of themselves throughout.