Diego Simeone's men, whose only top-flight defeat this season came back in September, missed a chance to wipe out the three-point gap to Barca ahead of the champions' trip to Getafe, but did at least maintain their two-point advantage over their third-placed hosts.
Wissam Ben Yedder broke the deadlock in the 37th minute at the Ramon Sanchez Pizjuan, shortly after Andre Silva had come within a post's width of doing so.
But Atletico were level just before the break courtesy of Griezmann's moment of brilliance, earning a point that will have suited the Camp Nou giants more than the two teams involved.
Sevilla dominated possession in the opening stages but it took until the 15th minute for the first shot in anger, Roque Mesa flashing a strike wide from an awkward angle.
Pablo Machin's team were almost caught on the counter-attack as Griezmann's swerving effort from 20 yards had Tomas Vaclik at full stretch to keep it out.
Sergio Escudero headed well over the crossbar after leaping to meet Jesus Navas' searching cross and Silva struck the woodwork with a fierce shot before Sevilla made the breakthrough.
The quick-thinking Daniel Carrico prodded Navas' cutback on to Ben Yedder, who turned and side-footed home to give his side a deserved lead.
It did not last long, though, with Griezmann's typically brilliant set-piece leaving Vaclik helpless.
There was an early exchange of chances at the start of the second half, Saul forcing a smart stop from Vaclik and Pablo Sarabia similarly calling Jan Oblak into action.
Former Sevilla forward Vitolo was brought on to jeers from the home crowd just before the hour mark but it was firm fans' favourite Ben Yedder who almost scored again, dragging a low shot just wide of the far post.
Griezmann spurned an excellent chance to win it eight minutes from time, shooting straight at Vaclik after racing through on goal, while Oblak denied Joris Gnagnon at the other end as a match featuring 12 yellow cards ended all-square.
Griezmann's quality shows in glimpses
Top-class players have it within themselves to dictate games, but when that proves impossible, they still find a way to make a mark. Griezmann did just that, punctuating an otherwise unremarkable display with a superb goal that ultimately wrapped up a hard-earned share of the spoils.
