Atletico entered the match knowing that a victory would see them cut the gap on league leaders Barcelona to three points ahead of El Clasico at the Bernabeu on Saturday afternoon.
However, Garcia netted an 88th-minute winner for Espanyol as Atletico suffered their first league defeat of the season.
Antoine Griezmann and Fernando Torres started up top for the away side, while Angel Correa and Kevin Gameiro were introduced in the second period as Diego Simeone's men desperately looked to make the breakthrough.
It was Espanyol that recorded just their fifth league win of the campaign, however, when Garcia collected a smart pass from Esteban Granero before finding the back of the net with a smart finish.
The visitors only managed one shot on target during the 90 minutes at the RCDE Stadium, and the defeat is a massive blow for a team that had been chasing down unbeaten Barcelona at the top of the table.