David Villa pounced on a Rayo error to open the scoring after just eight minutes, and Turan doubled the lead after half an hour, soon after the home side's Jonathan Viera saw his penalty saved.
Viera somewhat compensated for his miss from the spot by reducing the deficit towards the end of the first half, but the hard work Rayo had done to get themselves back in the game was quickly undone by slack defending from a free-kick, which led to Turan's second goal and Atletico's third.
An own goal by Saul Niguez after 75 minutes made sure of the points for Diego Simeone's side, with Joaquin Larrivey scoring the second Rayo consolation.
Rayo made a bold start to the match but it was Atletico who had the first chance, Diego Costa shooting wide.
The opening goal came when Rayo tried to play the ball out from the back following a goal kick.
Raul Baena came under quick pressure from Villa, whose challenge led to the ball falling to Costa in the area, and the Brazilian played it back to his fellow striker who tucked into an open goal, scoring for the second time in two league games.
Rayo were presented with a way back into the game almost immediately after the goal when they were awarded a penalty, with Alberto Bueno tripped at the heel by Javier Manquillo in the area.
But not for the first time this season, Paco Jemez's side failed to take advantage of a gift, Viera's penalty pushed away by Thibaut Courtois.
Rayo goalkeeper Ruben Martinez made a double save to deny Costa and Jose Sosa, but there was little he could when his team's high defensive line was exposed and punished by the visitors.
Villa set Costa free down the right wing and the Brazilian was able to hold the ball up just as he entered the box, pulling it back to Sosa, who squared for Turan to control and tap into an empty net.
Rayo managed to pull a goal back five minutes before half-time. The danger was created by a rare accurate cross from Lass Bangoura on the right wing. It was met by Larrivey, who played it back to Roberto Trashorras and then Viera's shot deflected past Courtois.
Larrivey could have levelled the score, as a scuffed clearance by an Atletico defender fell straight to him, but the Argentinian was unable to get enough power on the shot to beat Courtois.
Atletico were able to restore their two-goal cushion right before the break. Gabi swung in a free-kick which was inadvertently headed towards the back post by a Rayo defender and Turan was able to guide the ball in from two yards.
The second half was less chaotic than the first, but Atletico still looked more likely to extend their lead than Rayo were to reduce the deficit.
The visitors' fourth goal arrived with 15 minutes remaining, Filipe Luis getting down the left side of the box and cutting the ball back for Costa to slide towards the far corner, but it took a nick off the toe of Saul on its way in.
Larrivey quickly responded at the other end, flicking on a lofted pass by Viera with his head and into the net.
It will take some turnaround from now until the end of the season if Rayo are to avoid relegation, as they stand six points from safety following Almeria's win over Getafe.
Atletico picked up their first win in three games to keep the pressure on title rivals Barcelona, but there was still some bad news for Simeone's side - 19-year-old midfielder Oliver Torres was forced to leave the pitch just four minutes after coming on as a substitute, due to what appeared to be a dislocated shoulder.