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 in the day, Atletico needed a victory to remain within a point of the Blaugrana, yet two missed chances from Alvaro Morata was the closest it came to claiming the spoils.
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, although the visiting keeper had to react sharply to get down to Antonio Puertas's 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 its frustrations for good, 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 was held to a seventh league draw of the campaign.