The deposed La Liga champions couldn't find a breakthrough as they ended their campaign with a point, while the visitors held on to their place in Spain's top flight
Granada were destined for the drop at various times on Saturday with other results going against them, but a point was enough to extend their stay in the top flight to five seasons as Almeria and Eibar went down with Cordoba.
Diego Simeone's side only needed a point to secure third spot – as well as a place in next season's Champions League group stage - and they got the job done in unspectacular fashion.
Neither side fashioned a clear-cut chance in a tense encounter which will not live long in the memory, but Granada will not care about that as they celebrate a great escape which looked so unlikely before they strung together three consecutive wins before this dire stalemate.
Atleti ended the season without a win in four matches, 12 months after they were celebrating being crowned champions and preparing for a Champions League final against Real Madrid.
Simeone, without Mario Mandzukic, Arda Turan and Fernando Torres due to injury, cut a frustrated figure on the touchline for much of the game and will now turn his attention to ensuring Atleti hit the heights of the 2013-14 campaign next season.
Both sides offered very little going forward in a cagey first half which lacked quality, with a frustrated Antoine Griezmann starved of service.
Piti gave Atleti a scare with a free-kick from wide on the right which evaded everybody and prompted goalkeeper Jan Oblak to berate his defence.
Ruben Rochina had an opportunity to ease the tension when he stood over a free-kick from 25 yards out three minutes before half-time, but the Granada striker's effort failed to test Oblak after Piti had been replaced by Fran Rico due to injury.
It was the same story early in the second half, as Atleti seemed content to sit behind the ball, although Koke finally brought a save out of Roberto with a long-range volley 11 minutes after the break.
Granada fans raised the noise inside the Calderon as news of results elsewhere going in their favour continued to filter through, while also in the knowledge that an Atletico goal could send them down.
But last season's champions never really looked likely to break Granada, with a draw all they needed to avoid an early start to the season in the Champions League play-offs.
The closing stages were played out by Granada's defence tapping the ball around their own half, and the final whistle was greeted by a pitch invasion as they celebrated an unlikely survival.