And Griezmann effectively killed off the match with another classy strike at the start of the second half, dinking the ball into the back of the net over goalkeeper Steve Mandanda after Koke had sprung him in the Marseille area.
We'll be showing FREE highlights right here on BTSport.com and the BT Sport app shortly after the final whistle has blown, while the enhanced video player will also continue to be available for subscribers who want to watch the game in full.
A victory for Los Colchoneros in this game would see them equal Sevilla as the team to have won the Europa League on the most occasions (three). At the end of the match Costa in the counterattack found Gabi, and he scored his first t-shirt "Atletico" in 2015.
Several Marseille players were in tears at fulltime, undone by a player who was rejected by several French clubs as a youth because of his diminutive stature.
The dominance of Spanish team could be further underlined if Atletico's neighbors, Real Madrid, triumph against Liverpool in the final of the Champions League in Kiev on the 26th of May.
The 27-year-old scored in each half in Lyons, before Gabi, the Atletico captain, struck late on to seal victory for the Spanish club.
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It changed the game and really put the pressure on them, then we got the second and won the game'. But for us, we've got to use that disappointment to look at things we need to do better.
"When we won the Europe League it gave us security and helped us grow", Simeone told a news conference.
He was in the Atletico side that lost on penalties to Real Madrid in the Champions League final in 2016 and lost the European Championship final with France that summer.
For them, former West Ham midfielder and now Marseille skipper, Dimitri Payet, is a key man, while their fans will be hoping defender Adil Rami is not distracted by his new girlfriend, former Baywatch bombshell, Pamela Anderson.
"I've been lucky to win a lot but when you have dreamt about something since you were a child it's different".
Officially, there will be 11,500 Marseille fans in the crowd of close to 60,000 in Lyon, but thousands more were expected to travel.
Notwithstanding the fact that Atletico possess some of Europe's finest players in Jan Oblak, Diego Costa, Koke and Griezmann, Diego Simeone's side are the flawless anti-thesis to the current definition of success in European footballing dynamics - they may operate on a limited budget, but European Cup finals are their staple hunting grounds.