The Colombian striker, top scorer in last season's Europa League with 17 goals as he led Porto to the title, netted the opener in the 23rd minute at a sun-bathed stadium after good work by former Arsenal winger Jose Antonio Reyes.
His second came from the penalty spot in the 36th after Brazilian Diego, another close-season addition to Gregorio Manzano's squad, had been felled in the box.
Atletico's third high-profile new signing, Turkey midfielder Arda Turan, then played Falcao through to complete his treble with a deft chip over goalkeeper Tono 10 minutes after the break.
Turan claimed his second assist with just over 10 minutes left when he crossed for substitute Adrian to glance a header past Tono for the home side's fourth to round off their first win of the campaign.
Real Zaragoza forward Luis Garcia had an eventful match against his former club Espanyol in Sunday's earlier kickoff, smashing in a stoppage-time winner for a 2-1 victory minutes after he seeing his penalty saved by Cristian Alvarez.
In Sunday's Madrid derby, promoted Rayo Vallecano claimed their first win of the campaign with a 1-0 success at Getafe.
