The home side controlled the match throughout, although it took until the 38th minute for them to break the deadlock. Centre-back Diego Godin flicked the ball on inside the area and Miranda was on hand to fire in from close range.
Granada's chances of salvaging anything from the game were hampered when Henrique was handed his marching orders for a late challenge.
Atletico made their numerical advantage count in stoppage time when Falcao turned in a cross from Juanfran following a quick counter-attack move.
The win has lifted Atletico up to seventh in the La Liga table.