The 22-year-old Slovenian pulled off two vital first-half saves, the first of them at point-blank range, to deny Gareth Bale and enable Atletico to extend their unbeaten record against Carlo Ancelotti’s men this season to seven games.
Real enjoyed the better of the early stages at the Vicente Calderon, but ultimately had to make do with a share of the spoils to set up a dramatic shoot-out at the Bernabeu next Wednesday evening.
Intriguingly, Atletico have won and secured two score draws in their three trips into enemy territory to date during the campaign, and a similar result would be enough to secure a semi-final berth for Diego Simeone’s side.
Real sprinted out of the blocks and had their hosts on the back foot from the off, with Bale in particular a threat as he and full-back Dani Carvajal prospered down the right.
Carvajal forced Oblak into a second-minute save with a long-range effort, but it was the Wales international who came closest to breaking the deadlock during the opening flurry.
He should really have scored with just four minutes gone when he took advantage of defender Diego Godin’s error to race in on goal, but Oblak threw out his right arm to make a fine save.
Cristiano Ronaldo failed to extend the keeper unduly with a 35-year-free-kick, but Bale did force him into another impressive save 14 minutes before the break with a skidding effort which bounced just in front of him.
Oblak distinguished himself once again six minutes later when he turned away James Rodriguez’s audacious effort, and opposite number Iker Casillas was called upon for the first time seconds later after Sergio Ramos had uncharacteristically gifted possession to Antoine Griezmann.
The second half, however, was a much more even affair as Atletico striker Mario Mandzukic started to make his presence felt – not always legally – although clear-cut chances were few and far between.
However, the introduction of Fernando Torres as a late substitute injected new life into the game as he had appeals for an 87th-minute penalty waved away and then saw Mandzukic blast a last-minute drive into Alvaro Arbeloa’s midriff.
Ronaldo scuffed an injury-time shot straight at Oblak at the other end, but there was to be no late drama as the game ended in stalemate.
Atletico Madrid: Oblak, Juanfran, Miranda, Godin, Siqueira, Turan, Mario Suarez, Gabi, Koke (Torres 83), Griezmann (Raul Garcia 77), Mandzukic. Subs not used: Moya, Tiago, Saul, Jesus Gamez, Gimenez.
Real Madrid: Casillas, Carvajal (Arbeloa 85), Varane, Sergio Ramos, Marcelo, Modric, Kroos, Rodriguez, Bale, Benzema (Isco 76), Ronaldo. Subs not used: Navas, Pepe, Khedira, Jese, Illarramendi.