Valencia were trailing 3-1 when seven minutes of time were added on but Hugo Duro scored twice in the final stretch of the game to salvage a point, to the delight of their raucous home fans.
Griezmann restored Atletico's lead in the 58th with a superb shot into the top corner from outside the box following a marauding run from his own half in undoubtedly the Frenchman's best moment of skill since returning to the club in September.
Sime Vrsaljko looked to have sealed the points with a scrappy goal from close range two minutes later that was initially ruled out and then awarded following a VAR review.
But Valencia came alive right at the end of the game, pulling themselves back into contention when substitute Duro slid in to meet a Jose Gaya cross and score in the first minute of stoppage time.
Duro then equalised in the fifth minute of added time with a towering header from a corner, deepening Atletico's problems after they were easily beaten 2-0 at Liverpool on Wednesday to leave their hopes of reaching the Champions League knockout stage hanging by a thread.
Atletico would have gone up to second in the standings with a win but instead are fourth on 23 points, four behind leaders Real Madrid after 12 games. Valencia moved up to 10th on 17 points.