The Rojiblanco side's build-up to the game was dominated by talk over Griezmann's future, with a €100 million summer move to Barcelona reportedly lined up.
Marseille had started brightly but found themselves 1-0 down to an Antoine Griezmann strike when Payet pulled up hurt.
Griezmann pounced in the 21st minute, slotting coolly into the bottom left corner after being set up by midfielder Gabi's first-time pass. Marseille's woeful defending contributed as midfielder Zambo Anguissa failed to control a needlessly casual pass out from goalkeeper Steve Mandanda and the loose ball bounced straight to Gabi.
Griezmann was in no mood to take things easy as he chipped home a delightful second just after the break.
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"Even diminished, he set up the (Valere) Germain chance. Against a team like Atletico you can not afford to fall behind as it becomes hard".
"We had the best chance first up and then we made a mistake that cost us a goal. Atletico are a great team and we have no reason to be ashamed of this loss".
The 27-year-old France global has been heavily linked with a move away from the Wanda Metropolitano this summer and showed his class as Atleti ran out comfortable 3-0 winners in Lyon.
"I've never given him anything", Simeone said to reporters in his post-match press conference, as per Marca.
"I don't know how to describe the finish (for the second goal) - perhaps cold-blooded".
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Football is handsome, but it can be cruel too, none so much as during an European Cup final. Now we are in the UEFA Super Cup, so he could play four finals with us. "We did so again tonight".
However, perhaps as a nod to the inevitable, Simeone thanked Griezmann for his service.
Simeone, who had to watch from the stands due to a touchline ban, called the victory a reward for his side's hard work and even expressed hope that Griezmann could be convinced to stay.
Atletico, who made their fifth appearance in the final of European tournaments in the past nine years, was crowned in the Europa League in 2010 and 2012, while Marseille anticipated for another European title after winning the Champions League back in 1993.
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