The home side were ahead inside five minutes as Diego Costa opened the scoring with a composed header from close range.
Raul Garcia had a goal ruled out for offside soon after as Granada struggled to control a confident Atletico attack.
Radamel Falcao doubled his side's advantage on 27 minutes, lashing into the bottom corner less than 90 seconds after nearly heading into his own net.
Falcao finished the contest early in the second half when he diverted Koke's free kick into the far corner for his 30th goal of the season.
Garcia then got in on the act to make it four as he controlled a bouncing ball to fire past Roberto into the roof of the net.
Full-back Felipe Luis added shine to the scoreline late on with a deft finish to claim his first goal of the season.
Granada failed to show any kind of resistance as Atletico momentarily moved level with Real Madrid on second place on 65 points.