The outcome of the game was never in doubt once the visitors went a goal and a player down after 19 minutes, Raul Baena shown a red card for bringing down Coro in the area and Edu Albacar scoring from the spot.
Paco Jemez's side could only seek to limit the damage for the remainder of the game and did a good job of it until Javi Marquez doubled the lead on 79 minutes.
The Madrid side had beaten Getafe in their last outing and had the opportunity to leapfrog their opponents and climb out of the relegation zone. Instead they slipped five points behind Elche, who picked up their first win in six games and moved up to 14th in the Primera Division table.
Fran Escriba's side began on the front foot, putting pressure on their opponents early on.
Rayo goalkeeper Ruben Martinez was called into action with just five minutes played, keeping out an effort from Carles Gil, and 10 minutes later had to get down low again to thwart Cristian Herrera.
Rayo had been second best up to that point, but showed signs they were capable of getting a positive result, until referee Pedro Jesus Pero Montero made a decision that severely hampered their chances.
Herrera attacked down the left side of the box and cut the ball back towards Coro, who fell when challenged by Raul Baena.
Perez Montero pointed to the spot and sent off Baena, to the fury of the Rayo players, with left-back Nacho picking up a yellow card for protesting the decision.
Former Rayo left-back Albacar struck a fine penalty into the top corner.
Ruben then had to make two saves from Aaron Niguez, who was playing against his brother Saul, to keep the deficit at one by the break.
The second half saw Elche up the pressure on the visitors, who were fortunate to escape Alicante without suffering a heavier defeat.
Ruben made three saves from Aaron, Coro and Damian respectively in the space of a couple of minutes, while Marquez blazed over with an open goal gaping and substitute Manuel de Moral also missed the target.
The hosts got the second goal they deserved with 11 minutes remaining, taking advantage of some over-ambitious play by Rayo in their own half.
Saul, whom Manchester United assistant coach Phil Neville reportedly flew out to see in action against Getafe last weekend, was caught in possession on the edge of the area by Richmond Boakye and the ball fell to Marquez, who stuck it beyond Ruben and into the bottom corner.