A pair of headers in the space of three first-half minutes from Uruguay international Cristhian Stuani had the Catalan club within touching distance of a remarkable triumph.
Victory seemed virtually assured for Girona after Griezmann collected a second yellow card for dissent immediately after being booked for diving, marking his first ever red card in LaLiga.
But substitute Angel Correa rifled in from the edge of the area at the end of a brilliant solo run in the 78th minute and a previously nerveless showing from Pablo Machin's men wobbled in untimely fashion.
Goalkeeper Gorka Iraizoz was culpable as Stuani's countryman Jose Gimenez converted Koke's free-kick and embarrassment was averted for Diego Simeone's side.
Both teams observed a pre-match minute's silence to honour the 14 people killed by Thursday's terror attacks in the region before Girona began in composed fashion.
Machin's men were methodical in their work, unruffled by failing to create early chances, and they hit the front after 22 minutes.
Borja Garcia worked possession back to Alex Granell, whose searching cross from the left was expertly headed home by Stuani.
Girona were in dreamland three minutes later as Stuani won a free-kick on the same flank and nodded in when Gimenez badly misjudged his clearance.
Yannick Carrasco tried to muster a response for the visitors, with former Athletic Bilbao keeper Iraizoz keeping out his bouncing effort from the edge of the box.
Remarkably, matters almost deteriorated further for Atletico four minutes before half-time.
Jan Oblak completed a double save by brilliantly changing direction to paw Borja's close-range effort off the line after Pablo Maffeo's deflected cross caused havoc.
Saul Niguez's 50th minute yellow card for hacking down tormentor-in-chief Stuani neatly summarised Atletico's frustration, although Griezmann – badly isolated during a first half where he was restricted to 12 touches – almost reduced the arrears with a spectacular overhead kick that flashed narrowly wide.
Simeone sent on attacking midfielder Correa in place of full-back Juanfran in an attempt to loosen Girona's firm grip on the contest, although an act of self-sabotage would see their evening unravel further.
Griezmann burst into the box and went to ground as Iraizoz plunged at his feet. Referee Juan Martinez Munuera deemed that to be simulation and the 26-year-old's apparently sharp tongue sealed his fate.
The type of inspiration moment Atletico might have hoped to see Griezmann produce belatedly arrived courtesy of Correa's stunning solo effort.
Girona responded by tearing up the other end, with Stuani spurning a hat-trick chance on the end of Portu's cross.
It was a miss he would regret when Iraizoz came for Koke's left-wing delivery and failed to get there as Gimenez planted a header into the net.
Marc Muniesa fired over as the hosts tried to salvage victory in stoppage time, while Olarenwaju Kayode – one of five loan signings from Manchester City – forced Oblak to excel himself once again in a breathless finale.
Dropped points in their opening matches against Alaves and Leganes left Atleti playing catch-up in last season's title race and, with two more games on the road to come and a Griezmann suspension to contend with, Simeone's relief with be tempered by anxiety over history swiftly repeating itself.
Key Opta stats:
- Atletico have not lost a season-opening game in La Liga under Diego Simeone (W2 D3).
- Atletico have come from two goals down to be unbeaten for the first time in La Liga since May 2009 against Espanyol (win by 3-2).
- Christian Stuani is the only player to have scored two headed goals in a La Liga game against Atletico under Diego Simeone.
- Besides, Stuani is the only player to have scored a brace against Jan Oblak in La Liga (Cristiano Ronaldo scored but it was a hat-trick).
- Atletico are unbeaten in their last 12 La Liga away games (W6 D6), the longest current run of any team in the competition.
- Atletico have conceded two headed goals in a La Liga game for the first time since April 2012 against Levante.
- Antoine Griezmann has been sent off in La Liga for the first time ever (253 appearances).
- Of players to have scored 100 per cent of their goals from inside the box in the competition, Christian Stuani has scored more goals than any other current La Liga player (44 from 44).
- Stuani has scored a brace on his La Liga debut for Girona and on his Premier League debut for Middlesbrough.
- Antoine Griezmann has failed to score in his last six La Liga games, his worst run in the competition in 2017.
- Angel Correa has scored more goals as a substitute than any other player in La Liga since 2015-16 (nine).