And, after Diego Simeone's charges struggled in their Champions League group opener, they were back to their best on Wednesday to down Club Brugge 3-1.
As usual, Griezmann was among the goals, hitting 28 minutes in to cancel out an early lead for the Belgians before doubling his tally in the second half.
That goal, moreover, was the 8,000th in the history of the Champions League, while Koke went on to seal Atletico's victory by making it 3-1 at the Wanda Metropolitano.
Griezmann therefore enters a distinguished group of players who have netted milestone goals since the European Cup was rebranded as the UEFA Champions League in 1992.
Other notable scorers include David Trezeguet, who scored the 3,000th goal in a 7-0 rout for Juventus over Olympiakos, and Peter Crouch, scorer of the 4,000th goal as Liverpool beat PSV Eindhoven 1-0 in April 2007.
With three years the mean time between each thousand goals, the race will now be on to see who takes the honour of the 9,000th - while it will not be long until we are in five figures.