The visitors had the majority of possession, but had few clear-cut chances throughout the remainder of the first half.
Fran Rico tried to capitalise on Vallecano's misses just before the break, but headed wide from close range.
Yacine Brahimi almost broke the deadlock early in the second half, but his shot from the middle of the box struck the crossbar.
However, the Granada striker was sent off just two minutes later when he was shown his second yellow card of the afternoon for a foul on Iago Falque.
The visitors were able to take the lead within three minutes of their opponents being reduced to 10 men as Saul Niguez drilled the ball in from outside the box.
Vallecano continued to created chances as full time approached, with Adrian forcing a save five minutes from full time with a sliced effort from a tight angle.
However, Seba Fernandez managed to find the target for a third goal for the away side moments later, heading into the bottom corner from a Larrivey cross to seal the win.