Tight security measures oversaw the first top-flight match in Catalonia since two terror attacks in the region left 14 dead and hundreds injured in Barcelona and the nearby seaside town of Cambrils on Thursday and the early hours of Friday morning.
Concrete road blocks were mounted outside the Estadi Montilivi as in both attacks vans had been used to mow down pedestrians.
However, a near capacity 13,500 crowd weren't dissuaded from attending and thought the hosts were headed for a dream start to their first ever La Liga campaign.
Atletico's hopes seemed to have gone when Griezmann was controversially dismissed 23 minutes from time.
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The French international appeared to have been clipped by Gorka Iraizoz as he rounded the goalkeeper, but was instead booked for diving and then shown a straight red card for his protests towards referee Juan Martinez Manuera.
Despite their numerical disadvantage, Atletico responded heroically to salvage an unlikely point as Angel Correa blasted into the top corner from outside the box 12 minutes from time.
"Many at 2-0 down in the first-half would have thought the game was over," said Atletico boss Diego Simeone.
"When we went down to 10 men that thought would have been doubled, but the team kept going in the same way they have the past few years with effort, a never say die attitude and kept going until the end."
The visitors still had their own goalkeeper Jan Oblak to thank as the Slovenian produced an outstanding reflex save to prevent Manchester City loanee Olarenwaju Kayode from netting a last-minute winner.
Clement Lenglet bundled the hosts in front from a corner midway through the half, but Leo Baptistao levelled 10 minutes before half-time.
Sevilla also ended with 10 men as Ever Banega was sent- off following an angry exchange with the referee.
Earlier, Real Sociedad also came twice from behind to beat Celta Vigo 3-2 at Balaidos.
Maxi Gomez had put Celta in front early in both halves, but goals from Mikel Oyarzabal, Juanmi and Willian Jose's penalty two minutes from time handed the Basques all three points.