Messi was barely a figure in the opening 20 minutes, touching the ball just six times as Fati ran riot down the left-hand side.
He then struck again four minutes later with another ice-cool finish.
For now though, the 17-year-old is savouring every minute playing alongside the Argentine, who has been playing a big role in the young attacker's development.
The second half was less of a spectacle with Barcelona unable to add to the scoreline despite chances for Messi.
"We must highlight the game and performance of Ansu Fati", the Barca boss said, according to the Metro and cited on Soccer Laduma.
After the 8-2 defeat to Bayern Munich in August, Messi told Barca he wanted to leave and that he thought he could do so for free per a clause in his contract.
Just a minute after coming on, the former Liverpool man assisted Marcos Llorente for Atletico Madrid's 4 goal of the game.
They played with more pace and freedom than for many parts of last season, launching quickfire counters as well as building from the back. The Uruguayan in his stint at the Blaugranas scored goals for fun, becoming the third-highest goal-scorer in the club's history.
"He has the grinta, we present it more, but he also has quality".
"From my perspective, when it comes to building a squad, I look for guys who know how to perform and who accept when they play and when they don't. The team was liberated", Simeone said, talking about how competing for starting positions could help the team improve.
The winger was a constant threat all night before being substituted in the second half and he would have been well deserving of the award.
Ousmane Dembele also came on for his first competitive appearance for Barca since last November after returning from hamstring surgery.
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