Atletico Madrid maintains eight points lead, ahead of Barcelona and Real Madrid in the La Liga table.
Marcos Lorente scored in the 63rd minute and Angel Correa in the 75th minute for Atletico.
Granada's Jangel Herrera equalized in the 66th minute. However, that did not last long.
Suarez returned early in the second half with a shot at the pole.
Atletico Madrid has 54 points from 21 games, while Barcelona and Real Madrid are just below Athletic with 46 points from 22 games.