The goalkeeper made several superb stops, twice denying both Gareth Bale and James Rodriguez as the visitors dominated possession in the opening period and looked to take a lead back to the Bernabeu for the second leg.
Diego Simeone???s men had a couple of chances at the other end as Arda Turan headed wide, but they couldn???t test Iker Casillas in an improved display in a second half which threatened to boil over after Mario Mandzukic came to blows with both Sergio Ramos and Dani Carvajal on separate occasions.??
Neither side could find the winner, meanwhile, as Atletico extended their unbeaten run against Real to seven as the draw sets up a fascinating second leg on April 22.
The visitors immediately looked to take the initiative and Bale, fresh on his return to the side, spurned a glorious chance in the first few minutes as he was played clean through, but Oblak closed down the Welshman and kept his curling shot out with a firm hand.
Mandzukic looked to be the main target for Atletico, but their long-ball tactic didn???t suit the striker who seemed to be lacking pace ??? something demonstrated by Raphael Varane???s ease in catching him despite surrendering a 10-yard headstart.
Carlo Ancelotti???s men continued to enjoy the lion???s share of possession but the hosts??? defensive organisation looked like it could frustrate them, and it took until the half-hour mark before Oblak was tested again.
Luka Modric brought down the ball superbly in midfield before laying off for Bale, who turned his man superbly before drilling a low 25-yard effort which the Atletico goalkeeper kept out with a fine stop.
Rodriguez called the Slovenian into action again as he curled an effort with the outside of his left foot, before Modric then fired over with the outside of his right.
The visitors then showed their danger on the counter as Varane raced forward with a devastating run before his ball across the box eventually fell for Rodriguez, who tested Oblak once again, this time with a low shot which the goalkeeper turned away with his left hand.
Simeone clearly targeted the second half as the time to strike, and his side came out for the second half with a lot more drive and determination.
Their improvement was nearly rewarded as Juanfran ??? who failed to get forward at all in the first half ??? swung in an excellent cross from the right, but Turan could only head wide of the near upright.
As the game went on it got scrappier and derby tensions rose after a fractious encounter between Mandzukic and Ramos, who the Atletico man claimed elbowed him in the face. The striker appeared to then be on the receiving end of a punch in the ribs from Carvajal but it went unnoticed by the officials as tempers threatened to boil over.
Chances seemed to dry up until Raul Garcia and Fernando Torres were introduced, and they caused problems for the Real defence as Casillas looked shaky in the air, but there was to be no winning goal and the sides go to the Bernabeu all square.