Negredo missed a host of chances as Sevilla dominated the first period, but they were eventually gifted a half-time lead moments before the break. Ruben Martinez rushed from his goal to clear but only succeeded in presenting the ball to Rakitic who chipped delicately into an empty net from 40 yards.
Rayo were level though six minutes into the second half as Fernando Navarro pulled down Alejandro Dominguez as he tried to connect with Roberto Trashorras' corner and Dominguez himself stepped up to send the ball low past Beto.
However, Sevilla were back in front just three minutes later as wonderful play from Jesus Navas and Coke set up Negredo to backheel the ball in from close range for his third goal in as many games over the past six days.
Sevilla held on despite having Rakitic sent-off for a second bookable offence in stoppage time.
Both managers had hinted before the game that the hosts could be afflicted by tiredness having played a fierce Copa del Rey semi-final first-leg against Atletico Madrid on Thursday night, but there was no sign of fatigue as Sevilla started the stronger.
Ruben denied Negredo from the first of three one-on-ones between the pair in the opening half after just six minutes before Beto was called into action to turn away a fierce effort from Javi Fuego.
Sevilla continued to have the majority of the play with Jose Antonio Reyes especially prominent and it was from the former Arsenal man's through ball that Negredo had another great chance to open the scoring but he did not quite get enough purchase on his chip over Ruben and Alejandro Galvez cleared off the line.
Negredo came close again moments later as this time his attempted lob over the goalkeeper was saved, but the former Rayo man did have an unwitting hand in the opener on 45 minutes as Ruben's hurried clearance rebounded off him straight into the path of Rakitic who had the easy task of lobbing the ball into the unguarded net.
All of the hosts' good work in the first half though was undone early in the second as Navarro was unusually punished for pulling Dominguez's shirt inside the area from a corner and Dominguez comfortably stroked home the resulting spot-kick for his third goal of the season.
Negredo did eventually find the net three minutes later though to restore Sevilla's advantage as he showed great improvisation to turn Coke's low cross from the right past the helpless Ruben.
Thereafter both sides had chances as Rayo flooded forward in search of an equaliser but the best opportunity again fell to Sevilla as Ruben produced a fantastic save to prevent Rakitic from scoring his second of the day before Jordi Amat bravely blocked Negredo's follow-up effort.
Rakitic's day though was spoiled in stoppage time as he saw a second yellow card for diving in stoppage time in an attempt to win a penalty and he will now miss the trip to the Santiago Bernabeu next weekend.