The 33-year-old, who toiled in the reverse fixture at the Wanda Metropoliticano, opened the scoring in the 53rd minute.
France global Griezmann, 27, has now scored on each of his last three league visits to the Bernabeu and has 18 goals in his last 20 games in all competitions.
Real are next in action on Wednesday night when they face Juventus in the second leg of their Champions League quarter-final.
Partey has blossomed into one of Atletico Madrid's standout players this term. However, Real have a healthy lead in the tie, making it something of a unusual move by the Real Madrid boss. Griezmann slipped in Lucas and then continued his run so he was perfectly placed to slide home the rebound after Keylor Navas had parried.
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"What we have done in this decade is tremendous, Atletico fans should be proud of how their team is competing".
Atletico's response was stunning and, after Navas pawed a speculative Saul Niguez shot to safety, they ensured Madrid's lead was short-lived.
Los Blancos came into the clash the more in-form side as they have recorded an impressive six wins from their last six games in all competition.
The 33-year-old was withdrawn after 63 minutes for a rest ahead of Madrid's Champions League quarter-final second leg against Juventus at the Bernabeu on Wednesday and was an animated observer from the bench as Sergio Ramos twice came close to a late victor - once with a free-kick pushed over by Jan Oblak and then with a header from the resulting corner.
On the other hand, Diego Simeone made a couple of changes to the side that played midweek against Sporting CP. "He keeps improving, we need him and we are coming to the most important part of the year, when all the effort done in the first months pays off or not".