In a repeat of last season's final, Real dominated for much of Tuesday's clash at the Vicente Calderon.
But in Oblak, they ran into a keeper in inspired form, with his superb fourth-minute save to deny Gareth Bale, through on goal, setting the tone for a tense evening in the Spanish capital.
The Slovenia international was particularly impressive in the first half as Real spent much of the opening 45 minutes on the front foot.
Oblak reacted well to Cristiano Ronaldo's fizzing free-kick in the ninth minute, and after a lull in chances, he did similar to deny Bale from distance.
The Atletico keeper then kept out two good James Rodriguez efforts before the break - the first a splendid strike from the outside of his left foot - while the hosts' only meaningful chance of the first half saw the in-form Antoine Griezmann shoot at Iker Casillas from the edge of the penalty area.
That saw the bloodied Croatia forward leave the pitch, and he was involved in another tangle with Dani Carvajal shortly after.
Mandzukic's tense second half continued when he elbowed Carvajal, perhaps in retaliation, before Atletico enjoyed their best spell in the latter stages.
Godin flicked over from close range before Atletico's Mario Suarez and Real's Marcelo were booked - with both cautions ruling the respective players out of the second leg.
The hosts mounted one last charge, as Turan saw his effort smothered by Casillas and Arbeloa blocked a Mandzukic strike but the two sides were forced to share the spoils - largely due to Oblak's brilliance.
