The away side then took the lead in the 36th minute as Inaki Williams tapped home after Jan Oblak had brilliantly tipped Mikel San Jose's shot onto the post.
In the 61st minute, amid cries of 'shoot' from the Wanda Metropolitano faithful, Thomas Partey let rip with a fierce long-range piledriver to level the scores.
READ MORE: Black Maidens thrash hosts Uruguay 5-0 in World Cup
The Basque club restored their advantage a couple of minutes later with a well-executed counter attack which saw Iker Muniain thread an inch-perfect pass to Williams who calmly slotted past the Slovenian goalkeeper.
Atletico continued to fight back and look for an equaliser and they managed just that with ten minutes to go, as Rodri, who was once again excellent, headed in a Thomas corner at the near post.
READ MORE: Black Maidens thrash hosts Uruguay 5-0 in World Cup
The drama didn't end there as the home side went on to claim a famous victory with Godin's last gasp header after VAR was put to good use.