Samu Garcia seemingly secured Malaga a vital win in their bid for a UEFA Europa League place and, although Griezmann netted his second 12 minutes from time to claim a point, a draw will unlikely prove particularly helpful in their bid to keep pace with leaders Barcelona and Real Madrid.
Despite hosting Real in the UEFA Champions League on Tuesday, Diego Simeone could not afford to rest key players and, for the first half an hour, Malaga caused few problems.
Indeed, it was the visitors who broke the deadlock in the 25th minute, Griezmann capitalising on a Carlos Kameni error to score his 17th league goal of the season – his best ever Liga campaign.
The champions failed to hold on until the break, though, as Fernando Torres directed a cross into his own goal and that spurred Malaga on in the second half, as Samu celebrated his new contract with a clever finish 19 minutes from the end.
Griezmann scored his second of the day seven minutes later to secure a point for Atletico, but the draw does little in their pursuit of Real and Barca.
Atletico began the brighter of the two sides and generally controlled possession during the early exchanges, although chances were infrequent.
The only real opportunity of the first 20 minutes fell to Torres, as a Juanfran cross dropped at the feet of the former Chelsea striker and he smashed his half-volley well over.
With chances few and far between it came as little surprise to see the opener come as a result of an individual error and it was Griezmann who profited.
Kameni failed to keep hold of Jesus Gamez's long throw-in and the France striker pounced, stabbing home from close range.
Malaga restored parity eight minutes before the break, though, and it came via an unlikely source.
Recio fired a powerful delivery in towards the near post from the left flank and Torres diverted it into his own goal, despite Jan Oblak's best efforts to keep it out.
Malaga came out full of purpose after the break, putting Atletico under intense pressure as they looked to take charge.
And they almost edged ahead in the 53rd minute, but Samu Castillejo could only direct Nordin Amrabat's cross just wide of the mark.
Despite finding themselves under the cosh, Atletico remained a potent threat on the break and went close a minute later, as Koke headed off target under pressure from Kameni.
Samu made Atletico pay for that miss, racing on to Amrabat's througball and clipping over the advancing Oblak to put Malaga ahead with 19 minutes left.
But there proved to be one final twist in the 78th minute, as Griezmann smashed home left-footed following a precise cut-back by Raul Jimenez.
