Atletico announced on Monday that Griezmann's loan return from Barcelona would be made permanent, and the France forward marked his first league appearance since with a composed second-half finish.
Alvaro Morata had earlier been denied an opener by a VAR review, but Griezmann's effort proved enough for coach Diego Simeone's men during a typically disciplined display. Athletic rightly had a late penalty award overturned.
The victory sees Atletico leapfrog its host into third place in LaLiga, trailing Barcelona and Real Madrid by three points ahead of Monday's (AEDT) El Clasico.
Inaki Williams headed over the crossbar when left unmarked from an early free-kick, and only a video assistant referee (VAR) review prevented Athletic from being punished for that miss after 10 minutes.
Morata appeared to have taken advantage of a slip from Yeray Alvarez before rounding Unai Simon to score, but on second viewing the referee ruled the Spain striker was guilty of a foul, much to Atletico's frustration.
Simeone's visitors failed to register a single shot between Morata's disallowed strike and half-time, but they hit the front within two minutes of the restart when Griezmann side-footed Morata's cut-back into the bottom-right corner.
Griezmann then miscued a volley after finding space at the back post, before injured goalkeeper Jan Oblak was replaced by Ivo Grbic in an apparent blow to Atletico's hopes.
Atleti was indebted to its substitute goalkeeper, however, when he made a spectacular save from Inigo Martinez's header. The visitors then survived late drama when a penalty was awarded for handball against Reinildo, with a VAR check showing the referee called that incorrectly, the ball having struck the defender's face.