Former Rayo player Coke headed in the only goal of the game on 58 minutes and Paco Jemez's side were unable to respond, even though Vicente Iborra was sent off for the visitors on 83 minutes, given a second yellow card for time wasting.
With fellow strugglers Getafe, Valladolid and Malaga all drawing over the weekend, this was a chance for Rayo to take a big step towards exiting the relegation zone, but instead they remain 19th in the Primera Division table, five points adrift.
Although Rayo had 74 percent possession in the first half, their dominance of the ball was not translated into chances.
Sevilla's tactics consisted of soaking up the pressure and using set pieces as their weapons.
Ivan Rakitic came close to scoring directly from a corner, his shot hitting the side netting of Ruben's goal.
Carlos Bacca had the ball in the net for the visitors but it was ruled out for a foul on Ruben in the build up.
Daniel Carrico then also had the ball in the net for Sevilla following a free-kick, but was correctly ruled offside, while Nico Pareja and Rakitic both missed the target with opportunistic efforts from distance.
Rayo's only chances in the first half were an overhead kick by Alberto Bueno that missed the target, and a cross shot from full-back Tito which never really troubled Sevilla goalkeeper Beto.
The second half saw more goalmouth action. Rakitic got into the Rayo area following a smart move by Sevilla but his shot was blocked by Ruben.
It had taken 54 minutes for the first clear chance of the game to arrive, but just two minutes later Rayo had their first real opportunity to score, Jonathan Viera shooting wide with just Beto to beat after playing a one-two with Iago Falque. Then came the goal. Rakitic sent a free-kick into the box and Coke rose highest to head past Ruben.
The ever attack-minded Jemez took off left-back Ravzan Rat for striker Samuele Longo in search of an equaliser, which opened up space for Sevilla to look for a second. Substitute Diogo Figueiras volleyed wide, and then Rakitic passed up a chance to finish off the game, missing the target when arriving at the far post to meet a cross from Diogo.
Viera and Larrivey squandered efforts for Rayo, who were given a brief boost when Iborra was sent off for a second yellow card with seven minutes remaining, the referee punishing him for taking too long to leave the pitch after he went down injured and received medical attention.
Rayo continued to dominate the ball but could create no further chances, even with four minutes of added time, slumping to their ninth home defeat of the season.