James Rodriguez put the Champions League winner in front, but an equalizer from Mario Suarez just minutes later set up what should be a tense second leg.
James put Madrid in front with a scrappy goal in the 81st minute and was on course to be the match winner until Garcia's close-range finish with just two minutes remaining.
Carlo Ancelotti made two changes to the starting team that claimed the UEFA Super Cup with a 2-0 win over Sevilla on Aug. 12. Xabi Alonso took Rodriguez's place in midfield and Marcelo came in at left back with Fabio Coentrao dropped to the bench.MORE: Ronaldo ice bucket challenge | Pitch invader's free kick | WAGs
In its first competitive game since losing to Real in the Champions League final, La Liga champion Atletico had just six players from that starting XI in the lineup again.
Pregame, a touching tribute was paid to Real Madrid great Alfredo Di Stefano, who died in July at the age of 88.
The hosts were the better and more lively of the teams early, pushing Atletico deeper into their own half, with rash challenges from Koke and Guilherme Siqueira seeing both yellow carded.
Mario Mandzukic and Saul had opportunities for Atletico soon after, but goalkeeper Iker Casillas stood firm to deny both efforts. Mandzukic had another decent chance after Casillas could only punch a clearance straight to him, but the Croatia international's attempted lob went straight into the goalkeeper's hands.
Gareth Bale almost opened the scoring two minutes into the second half as he forced Atletico goalkeeper Miguel Angel Moya into a strong save from an angle. Moya was needed again in the 68th minute as he pushed away a powerful Bale free kick, before Toni Kroos volleyed the rebound well over from inside the area.
Karim Benzema put a header onto the roof of the net before Rodriguez, who replaced an anonymous Cristiano Ronaldo at halftime, made the breakthrough.
Kroos played Daniel Carvajal in down the right and his cross was aimed for Benzema before a scramble led to Rodriguez finishing via a deflection.
But Atletico would find a way in the 88th minute as Garcia tapped in Koke's corner after being left unmarked right in front of Casillas.
Real had a penalty shout turned down late in the encounter as it was left on the back foot heading into the second leg.