Renan Lodi's first Atleti goal had put Diego Simeone's side ahead an hour in at Nuevo Estadio de Los Carmenes, sparking into life what had previously been a drab encounter.
Jan Oblak was called into action to deny Granada an opener midway through the first half, but - after the home team's coach received his marching orders - Atleti's goalkeeper could do little to prevent German finding the net.
With Barca rallying to beat Leganes earlier on Saturday, Atletico needed a victory to remain within a point of the pacesetters, yet two missed chances from Alvaro Morata cost them as they were unable to claim the spoils.
1 - No side has scored more goals from set-pieces than Granada in @LaLigaEN this season (10, level with Barcelona). Indeed, no side has scored more goals from corners than Granada (five). Strategy. pic.twitter.com/MwvI8M0yJA— OptaJose (@OptaJose) November 23, 2019
Angel Correa was inches away from nudging Atleti ahead in the third minute but could not stretch far enough to connect with Vitolo's deflected shot across the face of goal.
It took Granada 27 minutes to test Oblak, though the visiting keeper had to react sharply to get down to Antonio Puertas' effort.
Vitolo and Correa combined after the restart, only for the latter to pull a first-time shot wide. Left-back Lodi - who has made a fine start to life at Atleti - made no mistake, however, keeping his cool to slot under goalkeeper Rui Silva.
Maxime Gonalons received a booking for his part in a tussle with Morata soon after, with Martinez then sent to the stands.
However, Granada used their frustrations to spur them on, German getting the better of Kieran Trippier to nod in from Angel Montoro's corner.
Morata failed to keep a header from six yards out on target and the former Chelsea striker then blazed over from Lodi's cutback, while substitute Dario Poveda failed to tuck home amid a goalmouth scramble as Atleti were held to a seventh league draw of the campaign.
What does it mean? Labouring Atleti look toothless
Joao Felix's return off the bench is a timely boost for Simeone, but with Diego Costa - who has struggled for form anyway - out for up to three months, Atleti's options up front look limited heading into a hectic stage of the season.
Without Antoine Griezmann to fall back on these days, the Atletico boss needs his available forwards to sharpen up if they want to keep pace with Barca and Real Madrid in the title race.
Lodi loving life in LaLiga
Full-back Lodi was left out for the 3-1 win against Espanyol last time out, but the 21-year-old marked his return to the starting XI in style with a well-taken goal, while he was also unlucky not to have an assist when he teed up Morata late on.
Morata's scoring streak ends
Morata had scored in each of his last six games for Atleti heading into Saturday's encounter, though seemed to have lost his shooting boots this time around. After sending a header over from point-blank range, he skied over another fantastic opening with 10 minutes to go.
Key Opta facts
- Atletico Madrid are unbeaten in their last 10 LaLiga matches (W3 D7), the longest current run of any side in the competition.
- No team has scored more goals from set-pieces situations than Granada in LaLiga this season (10 - level with Barcelona). Indeed, no side has scored more goals from corners than Granada (five).
- Atletico have drawn four consecutive LaLiga away games for the second time in the Diego Simeone era, the other occasion coming between September and December 2018.
- Hector Herrera made 13 recoveries against Granada, the most by an Atleti midfielder in a LaLiga fixture so far this season.
- Atletico boss Simeone has never lost against Granada in LaLiga, winning 10 games, drawing two and keeping a clean sheet in nine of those matches.