Atletico took a 63rd-minute lead through substitute Jorge Koke but Betis looked to have snatched victory from the jaws of defeat when their own replacements Alejandro Pozuelo (86) and Jonathan Pereira (88) netted in quick succession to put the hosts 2-1 up.
However, there was to be another late twist in the tale when, from a corner four minutes into injury time which saw Atletico goalkeeper Thibaut Courtois sent up into the Betis area, Falcao headed home from close range to level the game up at 2-2.
Atletico came into the match in buoyant mood having booked their spot in the Europa League final in midweek and having won four successive matches, and they will wonder how they failed to make it five wins on the trot on Sunday as they chase a top four finish in La Liga.
The Rojiblancos dominated in terms of chances and it was a surprise that they had to wait until almost an hour in to take the lead.
Falcao saw two first-half efforts go just wide while Gabi fired a 25-yard effort inches over and Adrian Lopez was denied by the feet of Betis goalkeeper Fabricio Agosto.
Adrian also saw a 41st-minute volley ruled out for a marginal offside.
It needed the arrival of Koke in the 58th minute for Atletico to finally break the deadlock, with the 20-year-old netting just five minutes after his introduction as he slotted in at the far post after Falcao had nodded down Tiago's deep cross.
It should have been 2-0 moments later after a superbly worked free-kick put Gabi clear on the edge of the box, but his low shot was well saved by Fabricio diving to his right.
Having survived that let-off, Betis then had a gilt-edged chance of their own seconds later as they immediately broke clear on the counter-attack, but Ruben Castro spurned the opportunity as his dink over Courtois went wide.
Gabi was denied again by Fabricio as Atletico sought a second goal, but just as the Rojiblancos looked set to see out a valuable 1-0 win, the home side turned the game on its head.
Pozuelo drew the teams level when he drilled Ruben Castro's lay-back into the roof of the net from eight yards out and then, while Atletico were still reeling, Betis took the lead when Pereira finished off a rapid move with a shot through the legs of Courtois, who may feel he could have done better.
Suddenly it was Atletico staring at defeat, but there was still time for them to snatch a draw thanks to the prolific Falcao, who headed home his 23rd league goal with the last incident of the match.