A host of Rayo's top performers left the cash-strapped club in the close season and Atletico were far superior on a sun-drenched evening at their Calderon stadium.
Raul Garcia stooped to head Diego Simeone's side in front from a Gabi corner in the 17th minute and Diego Costa made it 2-0 three minutes later when he struck from Arda's assist.
Costa, who had another excellent game, turned provider in the 35th minute when he sent Arda clear with a deft flick and the Turkey international rounded Rayo goalkeeper David Cobeno and stroked the ball into the net.
The heavily bearded Arda, given a rousing ovation when he was replaced with around 20 minutes left, capped a fine performance when he floated a cross over from the left for an unmarked Tiago to nod in a 53rd-minute fourth.
Spain forward David Villa, who joined Atletico from Barcelona in the close season, had a frustrating night and cracked a first-time shot against the bar in the 78th minute before Garcia scored his second in the 90th.
Sevilla drew 0-0 at Levante, while Real Betis were beaten 2-1 at home to Celta Vigo in the late game.