Girona looked set to enjoy a dream top flight bow when Uruguay international Christian Stuani rose to head in a sweeping cross from Alex Granell midway through the first half and three minutes later showed his predator's instinct to nod in a loose ball from close range.
Argentine forward Angel Correa pulled one back for Atletico with a long range strike in the 78th minute, after Griezmann had been dismissed for two successive bookings, one for diving to try and win a penalty and another for dissent.
Defender Jose Gimenez then beat Girona goalkeeper Gorka Iraizoz to Koke's chipped free-kick to head Atletico level in the 85th minute and cap a thrilling encounter at the Montilivi stadium, which was hastily expanded for the club's first Liga game.