The Croatian scored the quickest goal in the competition's history to earn the La Liga champions a 2-1 aggregate advantage in the tie, as he ghosted through Real's defence after just 81 seconds of play.
Antonie Greizmann, making his first start for Atletico, won a flick-on on the edge of the box and Sergio Ramos and Raphael Varane failed to win the following aerial ball to allow Mandzukic to fire into the bottom corner past Iker Casillas.
James Rodriguez, who netted for Los Blancos in the 1-1 first-leg draw, had their two best chances in the opening 45 minutes at the Vicente Calderon Stadium, but shot straight at Miguel Angel Moya after driving into the box before heading Luka Modric's cross wide.
Moya was also forced to save from Gareth Bale after the Welshman made an intelligent run off the right flank to collect a Toni Kroos pass, but he could not bend the ball around Atletico's new number one.
Atletico boss Diego Simeone, just as he was in the Champions League final between the two clubs in May, was sent to the stands midway through the half for his behaviour on the touchline.