Elche raced into a 2-0 lead at the Santiago Bernabeu thanks to goals from Lucas Boye and Pere Milla.
But two goals in the last eight minutes rescued what could be a vital point for Madrid.
Luka Modric dispatched a penalty before Eder Militao equalised deep into stoppage time.
This ensured Madrid still hold a four-point lead over Sevilla at the top of La Liga.
They also trailed 2-0 and managed to limit the damage thanks to goals from Papu Gomez and Oliver Torres in the final 20 minutes, but they were unable to build on their momentum to take the victory.
Atletico Madrid produced a miracle comeback of their own on Saturday to keep their hopes of finishing in the top four in the La Liga table firmly on track.
Atleti trailed 2-0 until the middle portion of the second half, and though Matheus Cunha pulled one back, they were still behind when the clock ticked to 90 minutes. In an incredible turnaround, though, Angel Correa and Mario Hermoso found goals in stoppage time to stun their opponent.
It pushed Atletico Madrid to 36 points and into fourth.
And as if there wasn't enough late goals this weekend, Barcelona snatched a crucial 1-0 win at Alaves thanks to Frenkie De Jong's 87th minute goal. That means Barca are only one point behind Atletico.
In Saturday’s other fixture, Cadiz heaped misery on Levante, who failed to build on their first win of the season last weekend as they succumbed 2-0 at home to another team in the drop zone.
Real Betis, meanwhile, remain comfortably ensconced in third place thanks to an easy 4-1 win over Espanyol on Friday. Here, too, there was a comeback, with the home side taking an early lead before a double from Borja Iglesias plus strikes from Guido Rodriguez and Willian Jose set up an easy win.
LA LIGA STATISTICS: