Atletico advanced 4-2 on aggregate in the round of 16, thanks to two goals by Marcos Llorente in extra time and another by fellow substitute Alvaro Morata.
The Catalan striker thrust his finger in the air before pumping his fist in celebration after scoring in the 78th minute. Messi had gone scoreless in his previous four appearances after being sidelined for five games with injuries.
Tottenham Hotspur moved eight points clear of Chelsea in the English Premier League with a 3-1 victory, the club's first win at Stamford Bridge since 1990.
Spain and Italy secure their places in the knockout stage of the Euro 2016 tournament with a game in hand while Turkey crashes out after failing to take any points from their first two games.
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