His first came after a period of sustained Marseille pressure to capitalise on a defensive error, before he doubled the lead after the break.
And in breaking down l'OM's resistance Griezmann broke new ground in European competition.
Griezmann is now the first French player to score two in a Champions League or Europa League final, including the European Cup or UEFA Cup forerunners of each trophy.
With 29 goals in all competitions this season, Griezmann has been vital to Atletico's season as the Colchoneros sit in second place in La Liga.
His opportunism was once again on show in Lyon, proving a lethal force in the Ligue 1 side's box.
Griezmann hit the net with each of his first two touches in the opposition area, forging a lead that Atletico did not squander on their way to a 3-0 win and Europa League glory.