The Europa League holders, fresh from last month's European Super Cup triumph against Champions League winners Chelsea, were ahead in the 29th minute at the Calderon when Mario Suarez struck from Diego Costa's low cross.
A quickfire treble early in the second half looked to have killed the game, with Koke and Arda Turan scoring from close range and Falcao adding the fourth from the penalty spot after a foul on Costa.
However, the home defence lost focus towards the end, incensing coach Diego Simeone and allowing Andrija Delibasic to score twice and Leo to add another a minute from time.
Rayo pressed for an unlikely equaliser but Atletico held out for a second win of the campaign.
Their goal tally from their last three outings now stands at 12 following a 4-0 La Liga win at home to Athletic Bilbao, when Falcao scored a hat-trick, and the 4-1 Super Cup success against Chelsea when the Colombian also netted a treble.
Granada and promoted Deportivo Coruna and Osasuna and Real Mallorca drew 1-1 on Sunday, while Real Sociedad beat visiting Real Zaragoza 2-0.