The in-form Colombia striker took his tally for the season to seven with a predatory goal and a penalty just after the re-start, lifting himself to the top of the La Liga goal-scoring charts ahead of Barcelona's Lionel Messi.
Substitute Diego Costa and Raul Garcia completed the victory as Betis finished with nine men, putting Europa League holders Atletico to 13 points from five games, two behind leaders Barcelona.
Betis took the lead after 25 minutes when Salvador Agra's cross bounced across the area and Atletico defender Miranda nudged the ball into his own net.
It only took Atletico two minutes to respond, Falcao sliding in at the far post to convert Raul Garcia's low cross shot.
Betis keeper Casto Espinosa kept his side in the game and before the break they re-took the lead, this time Juan Carlos's low cross ballooning into the Atletico net off defender Juanfran.
Atletico were quickly level again. Falcao was brought down for a penalty just after the re-start, resulting in a harsh red card for Betis defender Damien Perquis, and the Colombian netted from the spot.
Falcao, struggling with a thigh strain before the game, was replaced by Costa and the Brazilian striker put Atletico ahead at the back post from a flicked-on corner.
The home side were further hindered in their attempts at a fightback when substitute Joel Campbell picked up a second yellow card in the 83rd after a bizarre incident when an Atletico player appeared to handle the ball in his own area.
Raul Garcia lashed in Atletico's fourth to leave Betis sixth with nine points after a game which was postponed earlier in the mont