The Turkey international struck twice as Diego Simeone's men made light of a serious injury to Oliver Torres to move back above Real Madrid and Barcelona.
David Villa opened the scoring at the Campo de Futbol de Vallecas before Arda Turan struck either side of Jonathan Viera's effort to help the visitors into a 3-1 lead at the interval.
A Saul own goal saw Diego Simeone's men pull farther clear and even though Rayo pulled a goal back through Joaquin Larrivey, the Rojiblancos held on to move back above Real Madrid and Barcelona in the standings.
Atletico made a dream start in the Spanish capital thanks to Villa. The Spain international took advantage of some dreadfully lax defending from Raul Baena on the edge of his own box to send the ball in the direction of strike partner Diego Costa. The Brazil-born forward shaped to shoot but cleverly laid it off to Villa, who finished emphatically into the top right corner.
Rayo should have leveled just three minutes later, though, when Javi Manquillo clipped Alberto Bueno in the area. The contact appeared accidental but the referee pointed to the spot all the same. However, Thibaut Courtois guessed correctly, getting down rapidly to his right-hand side to parry Viera's penalty away to safety.
The hosts were punished for their profligacy on the half-hour mark when Arda was left with an open goal after good work from Costa and Jose Sosa on the right flank.
Rayo did pull a goal back when Viera made amends for his penalty miss by firing home with the aid of a deflection, after terrific link-up play involving Larrivey and Roberto Trashorras.
However, Atletico restored its two-goal advantage just before the break, Arda popping up at the back post to stab home a Gabi free kick from wide on the left touchline.
The Rojiblancos rarely looked troubled in the second period, though they were dealt a blow in the 68th minute when Oliver Torres, who had only just come on as a substitute, was stretchered from the field in obvious agony after suffering a suspected dislocated shoulder.
Simeone's side made light of the injury, though, and made it 4-1 with 15 minutes remaining when Saul, under intense pressure from Costa, put Filipe Luis' fine ball across the area through his own net.
Rayo pulled a goal back almost immediately, with Larrivey connecting brilliantly with Viera's in-swinging cross from the left wing to beat Courtois with a well-placed header, but there was to be no dramatic comeback, as Atletico saw the game out to once again move a point clear of second-placed Madrid ahead of third-placed Barcelona's game in hand at Malaga.