Fran Rico put the visitors ahead with a free-kick on 35 minutes and Paco Jemez's side were dealt another blow before half-time as full-back Nacho was sent off for receiving two bookings, the latter for diving to win a penalty.
Rayo fought hard for an equaliser for the remaining 45 minutes despite their numerical disadvantage, but lost all hope when Riki added a second for Granada in the 88th minute.
The Madrid side are just one point above the releagation zone but the bottom three all play later this weekend.
Granada, meanwhile, move up to 10th in the Primera Division and on to 20 points, approximately half the amount normally considered necessary to avoid relegation.
The first few chances of the game consisted of speculative efforts from distance until Youssef El Arabi squandered a glorious chance, somehow hitting the post from a couple of yards out when he had the whole goal to aim at.
Yacine Brahimi raced down the left-hand side on the break and, with Rayo goalkeeper Ruben flying out of the area, switched the ball to El Arabi, who dribbled towards goal and made the angle even harder for himself, striking the post and making himself a strong contender for miss of the year.
His error was forgotten by his team-mates four minutes later, however. Rico sent a free-kick into the box which evaded everybody, including El Arabi, and went straight into the net.
Alberto Bueno was denied an equaliser by Granada stopper Roberto a few moments later and then Rayo were reduced to 10 men when Nacho was given his second booking in five minutes.
It was the second home match in a row in which Rayo have had a man sent off in the first half.
The hosts did well in the circumstances and nearly drew level in the second half, Roberto again thwarting Bueno.
But with time running out Granada launched another break and Riki ran towards goal unchallenged taking the ball beyond Ruben, and even though he was felled by Johan Mojica as he approached the net, the ball still trickled over the line.