The best chance of the opening stages fell to the in-form Falcao, but the Colombian striker fluffed his lines following good work by Filipe Luis.
Despite Granada's superior possession, the home side struggled to carve out any decent opportunities in what was a dull first half. However, they nearly broke the deadlock before the break when Gabriel Torje's effort came back off the post.
The visitors finally found the net with an hour played as Arda Turan was on hand at the back post to convert Luis's cross.
Falcao could have doubled his side's advantage soon after, but he flashed his shot wide.
Atletico's night was soured in the 73rd minute as Suarez was sent off for a second yellow card of the match.