The midfielder's strike gives Diego Simeone's side a narrow advantage heading into Friday's reverse fixture at the Vicente Calderon Stadium.
Iker Casillas made early saves from Mario Mandzukic and Saul as the 2013-14 La Liga champions started brightly, before Cristiano Ronaldo headed a Gareth Bale cross just wide of the post on 43 minutes.
The Portuguese superstar was withdrawn at half time with an apparent injury concern, allowing £63m summer signing from Monaco James to join Bale and Karim Benzema in Real's star-studded attack.
Bale shot straight at Miguel Angel Moya five minutes into the second period, and later his free kick was parried by the Atletico keeper into the path of Toni Kroos, only for the German to blaze over from close range.
Like James, Kroos was making his full debut for the European Champions, but struggled to have an impact and the Colombian World Cup star's 81st-minute opener summed up the scrappy nature of the contest.
James tucked the ball into the bottom corner from inside the box following a goalmouth scramble, but Atletico did not lie down as Garcia bundled an equaliser over the line from a late corner.