Atletico survive dramatic Rayo comeback
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.
Barcelona top the table with the only perfect record in La Liga on 12 points from four matches after hammering Getafe 4-1 away on Saturday.
Malaga are second with 10 points after their 3-1 triumph over Levante, while Atletico, in fifth, have seven and have played one game fewer.
Stuttering champions Real Madrid are 11th with four points following their 1-0 defeat at Sevilla.
Spain striker Fernando Llorente scored within moments of coming off the bench as he returned to help Athletic Bilbao grab a thrilling 3-3 draw at Espanyol in the early kick-off.
The 27-year-old known as "Lion King", who asked for a transfer in the close season and had been linked in the media with a move to Juventus, was brought on for his first appearance in the league this season after 69 minutes.
With his side losing 2-1, he broke away on the left two minutes after entering the fray and fired low across the goal to equalise, celebrating with a huge roar to the small contingent of travelling fans.
Llorente told Spanish radio station Cadena Ser he was still planning to seek a new club in the winter transfer window.
"In January I am free to negotiate but I want to put that to one side for now to help the team," he said.
"I will always be an Athletic man, even though there will come a time when I am not playing for the team," he added.
Espanyol had stormed ahead in the first half with goals from Javi Lopez and Joan Verdu.
Bilbao started their fightback when Aritz Aduriz headed home in the 56th but, after Llorente levelled, Samuele Longo sprinted clear to net a third for the hosts with 10 minutes remaining.
Longo was sent off after picking up a second yellow card as he celebrated with Espanyol fans in the stands, and Aduriz bagged his second goal with a spectacular volley soon after to earn a point for Bilbao.
Marcelo Bielsa's side, who reached the fina