PSG host relegation battling Le Havre on Saturday
Garcia sealed the game for the visitors when he opened the scoring in the seventh minute, receiving the ball inside the box and rifling it past goalkeeper Marc-Andre ter Stegen to a wave of whistles at the Camp Nou.
Barcelona failed to convert a number of golden chances despite going agonisingly close to an equaliser.
Real Madrid now need only one point from their last five games to secure the title, while Barcelona are second on 63 points, 15 behind Real and level with Sevilla in third.