Ivan Rakitic, who was later sent off, lobbed their opener from 35 yards out, and Alvaro Negredo backheeled a cheeky second after Rayo Vallecano's Alejandro Domínguez had levelled from the penalty spot.
Negredo had also assisted Rakitic's goal in the 47th minute.
Sevilla ended on a sour note when Rakitic was given a red card in the 92nd minute.
Los Nervionenses are in 11 place, and in striking distance of Rayo Vallecano in sixth with a record of eight wins, nine losses and five draws leaving them five behind after 22 games.
The Rayistas are holding down a spot in the Europa League in sixth place with a record of 11 wins, 10 losses and one draws for 34 points.
Málaga and Real Zaragoza cancelled each other out as their match ended in a 1-1 draw.
Helder Postiga put Los Maños on the board with his effort in the 13th minute, but Isco scored in the 23rd minute to even the score at 1-1.
Real Zaragoza's José Mari was sent off deep into injury time at the end.
In the late match Real Sociedad turned on the style in the second half to earn a 3-0 win over Real Mallorca.
Mallorca had Javi Marquez sent off just before the half-hour mark, but held on until Gonzalo Castro broke the deadlock ten minutes into the second half.
Carlos Vela and Diego Ifran then added goals on 70 and 88 minutes respectively.
Real Sociedad, who had 67 per cent of the possession, are in eight place, and in striking distance of Valencia in sixth while Mallorca are currently in the relegation zone, four points behind 16th-place Granada.